This paper presents an optimization method using a genetic algorithm to solve the task assignment problem of achieving the shortest project duration for an engineering project with capital limit under mixed work calendars. Firstly, the problem was described. Then, a genetic algorithm was designed to solve the researched problem. A time reckoning mechanism based on the contractor's work calendar was proposed and related time reckoning functions were designed as the basis of calculating project duration for an engineering project under mixed work calendars. An integer coding method based on contract number was used to encode the chromosome. The refusal strategy was used in the population initialization to ensure the feasibility of chromosomes. To ensure the feasibility of offspring chromosomes, an improved crossover operator was used in the crossover operation based on the two-point crossover method, and a refusal strategy was used in the mutation operation based on the single-point mutation method. Finally based on the critical path method, the forward reckoning function FC was used to get the shortest project duration. The effectiveness of the proposed method was verified by a case study.