Hamsi is one of 14 remaining candidates in NIST's Hash Competition for the future hash standard SHA-3 and Hamsi-256 is one of four kinds of Hamsi. In this paper we present a genetic algorithm to search near collisions for the compress function of Hamsi-256, give a near collision on (256 - 20) bits and a near collision on (256 - 21) bits with four differences in the chaining value, and obtain a differential path for three rounds of Hamsi-256 with probability 2⁻²⁴, 2⁻²³ respectively, which are better than previous work reported about near collisions.