Real time convolution has many applications among others simulating room reverberation in audio processing. Non-uniformly partitioning filters could satisfy the both desired features of having a low latency and less computational complexity for an efficient convolution. However, distributing the computation to have an uniform demand on Central Processing Unit (CPU) is still challenging. Moreover, computational cost for very long filters is still not acceptable. In this thesis, a new algorithm is presented by taking advantage of the broad memory on Graphics Processing Units (GPU). Performing the computations of a non-uniformly partitioned block convolution on GPU could solve the problem of work load on CPU. It is shown that the computational time in this algorithm reduces for the filters with long length.