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Assembly sequence planning (ASP) becomes one of the major challenges in product design and manufacturing. A good assembly sequence leads to reduced costs and duration in the manufacturing process. However, assembly sequence planning is known to be a classical NP-hard combinatorial optimization problem; assembly sequence planning with many product components becomes more difficult to solve. In this paper, an approach based on a new variant of the Gravitational Search Algorithm (GSA) called the multi-state Gravitational Search Algorithm (MSGSA) is used to solve the assembly sequence planning problem. As in the Gravitational Search Algorithm, the MSGSA incorporates Newton's law of gravity and the law of motion to improve solutions based on precedence constraints; the best feasible sequence of assembly can then be determined. To verify the feasibility and performance of the proposed approach, a case study has been performed and a comparison has been conducted against other three approaches based on Simulated Annealing (SA), a Genetic Algorithm (GA), and Binary Particle Swarm Optimization (BPSO). The experimental results show that the proposed approach has achieved significant improvement in performance over the other methods studied.