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Planning of base stations (BS) is one of the fundamental problems in the fourth generation (4G) wireless network design. A new mathematical model for the 4G BS planning is proposed in this paper. The co-channel interference, orthogonal frequency division multiplexing (OFDM), the cell edge rate, the reference signal received power (RSRP) and the base station density are considered in detail in this model. The objectives of the model are to minimum construction cost, maximum coverage and capacity at the same time. It's a multiobjective optimization problem with constraints. So a multiobjective algorithm with a local search operator is designed to solve this model. Simulation results show that the according algorithm with local search operator can give a set of solutions with relatively lower cost, larger coverage, larger capacity and faster speed than the algorithm without local search operator. The effective and efficient of the proposed model can also be identified by the comparison of the solutions.