The partial-period autocorrelation of sequences is an important performance measure of communication systems employing them, but it is notoriously difficult to be analyzed. In this paper, we propose an algorithm to design unimodular sequences with low partial-period autocorrelations via directly minimizing the partial-period integrated sidelobe level (PISL). The proposed algorithm is inspired by the monotonic minimizer for integrated sidelobe level (MISL) algorithm. Then an acceleration scheme is considered to further accelerate the algorithms. Numerical experiments show that the proposed algorithm can effectively generate sequences with lower partial-period peak sidelobe level (PPSL) compared with the well-known Zadoff-Chu sequences.