Given that the narrator is a mad, clearly very excitable man, the mood of the story is one of nervousness and apprehension at what is to come. The reader feels the jumpiness of the narrator, his eagerness to tell his story but also eagerness to have the reader understand that he is not, in fact, mad. This sense of a desire to please also has an influence on the mood, making it somewhat cloying as the narrator attempts to gain the reader's favor.
Underlying it all is a mood one might label simply as evil. The narrator's desire to prove his rational nature and to suggest that somehow this desire or decision to kill his neighbor simply "entered his mind" is not sufficient to cover up the brutality of the murder he commits.