High temperature superconducting (HTS) bulks or stacks of coated conductors (CCs) can be magnetized to become trapped field magnets (TFMs). The magnetic fields of such TFMs can break the limitation of conventional magnets (<2 T), so they show potential for improving the performance of many electrical applications that use permanent magnets like rotating machines. Towards practical or commercial use of TFMs, effective in situ magnetization is one of the key issues. The pulsed field magnetization (PFM) is among the most promising magnetization methods in virtue of its compactness, mobility and low cost. However, due to the heat generation during the magnetization, the trapped field and flux acquired by PFM usually cannot achieve the full potential of a sample (acquired by the field cooling or zero field cooling method). The multi-pulse technique was found to effectively improve the trapped field by PFM in practice. In this work, a systematic study on the PFM with successive pulses is presented. A 2D electromagnetic-thermal coupled model with comprehensive temperature dependent parameters is used to simulate a stack of CCs magnetized by successive magnetic pulses. An overall picture is built to show how the trapped field and flux evolve with different pulse sequences and the evolution patterns are analyzed. Based on the discussion, an operable magnetization strategy of PFM with successive pulses is suggested to provide more trapped field and flux. Finally, experimental results of a stack of CCs magnetized by typical pulse sequences are presented for demonstration.