Evolution process and properties of wave-particle quantum walk (QW) are studied by theoretical calculation and quantum simulator's simulation. Quantum control can contribute to the realization of QWs in quantum wave-particle superposition state with a relative phase between walkers. The post-selection operation is used to realize the continuous transitions of QW from the state of waves with multi-path coherence to the state of particles without coherence in two different ways: coherence and mixing. Due to quantum interference, there are essential differences between coherence and mixing, and their specific features are characterized by position variance. We also demonstrate the coherent wave-particle QWs in the real quantum simulator. When the walker is in the wave-particle coherent state, two completely different properties can be observed simultaneously through one measurement. By adjusting the relative phase in the wave-particle coherent state, the diffusion rate of the walker can be controlled.