For the purposes of discussion, it will be assumed that the question does not refer specifically to Audrey Kurth Cronin's 2012 article in the journal Orbis titled "U.S. Grand Strategy and Counterterrorism." Instead, this answer will focus on the U.S. Government approach to countering terrorism as laid out in government documents and statements.
Presidents do not speak in terms of "grand strategies"; academics use that phrase in attempting to articulate long-term visions for how to defeat a major adversary -- during the Cold War, it was fear of the Soviet Union. Most analysts, however, recognize that "grand strategies" are not consistent with democratic political systems and values, as they require an authoritarian approach to directing foreign and national security policies, which is contrary to the ebbs and flows that accompany a political system where elections every two to four years can fundamentally alter the political landscape.
In the midst of his expansion of U.S. forces in Afghanistan, on May 22, 2010, President Obama laid the groundwork for a new strategy to counter terrorists in a speech at the United States Military Academy at West Point, New York. President Obama alluded to his vision for how to prevail against al Qaeda by referring to the final drawdown of U.S. forces in Iraq then underway:
"We will continue to advise and assist Iraqi security forces...And a strong American civilian presence will help Iraqis forge political and economic progress. This will not be a simple task, but this is what success looks like: an Iraq that provides no haven to terrorists; a democratic Iraq that is sovereign and stable and self-reliant." [Emphasis added]
The goal was clear: to stabilize war-torn countries riven with ethnic, tribal, and religious divisions that no longer provide an environment in which terrorist organizations like al Qaeda can take root. Longer-term, President Obama articulated the strategy as follows:
"Now even as we fight the wars in front of us, we also have to see the horizon beyond these wars -- because unlike a terrorist whose goal is to destroy, our future will be defined by what we build...to get there we must pursue a strategy of national renewal and global leadership. We have to build the sources of America's strength and influence, and shapea world that's more peaceful and more prosperous."
On June 28, 2011, the Obama Administration formally released its National Strategy for Counterterrorism. This document represents the most official U.S. Government statement on counterterrorism policy to date. In it, the document states, "The preeminent security threat to the United States continues to be from al-Qa'ida and its affiliates and adherents." [Emphasis in original] The White House laid out its strategy for defeating the threat of al Qaeda by "adhering to U.S. core values," including respect for human rights, helping other countries govern through democratic principles, respecting civil liberties at home, and finding the proper balance between security and openness in government. In addition, the U.S. would work closely with other countries in a partnership arrangement rather than dictating to them and would work through existing multilateral institutions.
The U.S. strategy would also involve elimating safe havens in poorly or ungoverned countries and countering al Qaeda's propaganda and recruitment practices. These are the basic components of the U.S. strategy for countering terrorism today.