Low Earth Orbit (LEO) satellites can provide high-speed and low-delay services for terrestrial users; however, the rapid movement of LEO satellites and the insufficient size of the LEO constellations incurs the instability of the transmission links. The rapid movement of LEO satellites also leads to frequent handovers. Fortunately, GEO/LEO heterogeneous satellite systems can remedy this shortcoming. As the handover decision strategy which makes the selection among the available satellites will directly impact the performance of GEO/LEO heterogeneous satellite systems, we propose a two-step access and handover decision strategy for heterogeneous satellite networks in this paper. Firstly, a GEO/LEO network selection is carried out based on utility functions that reflect user’s QoS requirements. Then, the multi-attribute decision making (MADM) method is used to select the specific LEO satellite if users select LEO satellite network. We also propose an Importance-TOPSIS scheme to improve the weight setting for handover attributes. Simulation results show that the proposed method can reduce the number of handovers and the forced termination probability of the system, and the overall throughput of the system is also improved.