The mixing process plays an important role in the combustion realization of the scramjet engine. In the current study, the steady jet, as well as pulsed jets with different wave shapes namely sine, square and triangle waves, is investigated in order to achieve adequate fuel/air mixing. Flow field properties are studied numerically based on grid independency analysis and code validation. The vortex structures, as well as the flow field parameters such as mixing efficiency, total pressure recovery coefficient, fuel penetration depth and mixing length, are deeply analyzed for different jet-to-crossflow pressure ratios. The obtained results predicted by the three-dimensional Reynolds-average Navier-Stokes (RANS) equations coupled with the two equation SST kappa - omega turbulence model show that the grid scale makes only a slight difference to wall pressure profiles for all cases studied in this article. Compared with the steady jet, the pulsed jets with different wave shapes are beneficial for the mixing efficiency improving of the transverse jet, and the pulsed jets have special advantages on reducing the total pressure loss and mixing length but not for improving the fuel penetration depth. When the jet-to-crossflow pressure ratio is high, the performance of pulsed jets is better, and different wave shapes in the pulsed jet result in different vortex structures. This should be studied and discussed deeply in the near future. (C) 2019 Elsevier Ltd. All rights reserved.