The word "grade" is not a proper noun so you would not capitalize it in order to state what grade you have completed. For example if you completed your schooling up to the 11th grade you would state "I completed grade 11."
Remember that in the English language only proper nouns are capitalized. A proper noun is any noun that names a person or place or thing such as a brand. For example shoe is a common noun but Nike is a brand so it is a proper noun. Girl is a common noun however Cathy is a specific person so this is a proper noun.
Either is acceptable depending on the document it is in. For example, in a résumé you would capitalize it. If you use it in a sentence, "I completed grade 1 at five years old," you wouldn't need to capitalize.