A fast algorithm for computing analysis window of real discrete Gabor transforms based on DCT in order to realize real discrete Gabor transforms efficiently was introduced. The original biorthogonal condition expression of computing analysis window functions was predigested by using the orthogonality of discrete cosine functions, and then divided the original equations set into a set of independent subsystems. Thus this algorithm can save a considerable computation. Some numerical experiments were given to demonstrate the efficiency and advantages of the proposed algorithm. It decreases the computational time compared to the original algorithm. 