The recognition of Handwritten Devanagari character plays a vital role in the research area. Number of approaches has been used in preceding researches and still it is being carried out ahead. In this research paper, Geometric and Zernike moment features of Devanagari basic and compound Character are used to recognize the handwritten character. Compound character is a special feature of Devanagari scripting; it joins two or more character in various ways forming a new character. The complexity and frequency occur in writing the compound character is more as compared to other languages. The proposed system is trained and tested on 27000 handwritten Devanagari basic and compound character database collected from different people. Each image is normalized to 30X30 pixel size. For recognition of Devanagari basic and compound character we have used MLP and KNN. The recognition rate is 98.78% and 95.56% which is comprehensive to the method.