Recently, expectations for camera-based document analysis and recognition have increased by improved performance of digital camera devices. In this paper, we propose a rotation angle estimation method using Gray-Scale Gradient Feature and Modified Quadratic Discriminant Function (MQDF). This method can recognize characters and estimate the rotation angle of those characters rapidly. As the result of the evaluation experiment using printed alphanumeric character, we have confirmed that the low dimensional feature vector is sufficient to estimate the rotation angle of characters. Also, we reduced the number of used eigenvectors of the covariance matrix to calculate the MQDF while keeping estimation accuracy.