Immersed boundary-lattice Boltzmann method (IB-LBM) has become a popular method for studying fluid-structure interaction (FSI) problems. However, the performance issues of the IB-LBM have to be considered when simulating the practical problems. The Graphics Processing Units (GPUs) from NVIDIA offer a possible solution for the parallel computing, while the CPU is a multicore processor that can also improve the parallel performance. This paper proposes a parallel algorithm for IB-LBM on a CPU-GPU heterogeneous platform, in which the CPU not only controls the launch of the kernel function but also performs calculations. According to the relatively local calculation characteristics of IB-LBM and the features of the heterogeneous platform, the flow field is divided into two parts: GPU computing domain and CPU computing domain. CUDA and OpenMP are used for parallel computing on the two computing domains, respectively. Since the calculation time is less than the data transmission time, a buffer is set at the junction of two computational domains. The size of the buffer determines the number of the evolution of the flow field before the data exchange. Therefore, the number of communications can be reduced by increasing buffer size. The performance of the method was investigated and analyzed using the traditional metric MFLUPS. The new algorithm is applied to the computational simulation of red blood cells (RBCs) in Poiseuille flow and through a microchannel.