U-lines are important parts of the Just-In-Time production system in order to improve productivity and quality. In real life applications of assembly lines, the tasks may have varying execution times defined as a probability distribution. In this study, a novel particle swarm optimization algorithm is proposed to solve the U-line balancing problem with stochastic task times. A computational study is conducted to compare the performance of the proposed approach to the existing methods in the literature. The results of the computational study show that the proposed approach performs quite effectively. It also yields good solutions for all test problems within a short computational time.