In this paper, a fast algorithm of discrete cosine transform-based interpolation filter (DCT-IF) for HEVC (high efficiency video coding) encoder is proposed. DCT-IF filter accounts for around 30% of encoder complexity, according to the computational complexity analysis with the HEVC reference software. In this work, the proposed DCT-IF is optimized by applying frame-level interpolation, SIMD optimization, and task-level parallelization via OpenMP on a developed C-based HEVC encoder. Performance analysis is conducted by measuring speed-up factor of the proposed optimization technique on the developed encoder. The results show that speed-up factors by frame-level interpolation, SIMD, and OpenMP are approximately 38-46, 3.6-4.4, and 3.0-3.7, respectively. In the end, we achieved the speed-up factor of 498.4 with the proposed fast algorithm.