Recently, a Sequential Optimization and Reliability Assessment (SORA) method was proposed and proven to be effective for solving reliability-based design optimization (RBDO) problems. In the SORA, the optimization loop and the reliability assessment loop are decoupled from each other. This helps improve the efficiency of the SORA significantly. However, the SORA still exists two main drawbacks: (1) the optimal solutions are easily trapped within local extremes and (2) the optimal results depend on the initial trial points. To overcome these drawbacks, this paper integrates the SORA with the Improved Constrained Differential Evolution algorithm (ICDE) to give a so-called SORA-ICDE for solving RBDO problems. Due to the global search mechanism, the SORA-ICDE can easily obtain global solutions regardless of initial points. The numerical results obtained in the paper are compared with available results in the literature to illustrate the efficiency, applicability and precision of the SORA-ICDE in solving the RBDO problems for truss structures.