Two-sided assembly line balancing problem (TALBP) is a vital design problem for the industries. In real production process, some complex constraints should be considered in the two-sided assembly line. To solve the practical TALBP, this paper proposes a hybrid algorithm (HABC) that combines the artificial bee colony (ABC) algorithm and late acceptance hill-climbing (LAHC) algorithm. In the proposed algorithm, a well-designed decoding scheme is embedded to tackle multiple assignment constraints. Moreover, two neighborhood search strategies are implemented by employed bee and onlooker bee to explore and exploit the new solution. A set of computational experiments is performed on benchmark problems. The comparison results, best solutions, standard deviation and relative percentage index demonstrate that the HABC algorithm outperforms other algorithms published in the literature and finds 5 brand new solutions for 15 instances.