It is difficult to make efficient decisions in manufacturing environments due to complexity and uncertainty which one can experience during most of the production phases. Although handling uncertainty is a difficult issue, it must be considered during modeling in order to obtain more realistic solutions for complex problems. One of the flow oriented production systems which is used in manufacturing is parallel assembly lines. They are preferred due to their flexible and productive nature. In this paper, parallel assembly line balancing problem with fuzzy parameters is studied in order to provide more realistic solutions in which the problem data is imprecise. A multi-colony ant algorithm for solving parallel assembly line balancing problems with fuzzy cycle and task times is proposed. Considering task times fuzzy is necessary especially in manual assembly operations. The fuzziness of the cycle time is related to task time variability. The proposed approach is tested on benchmark problems and solutions are presented.