Short-crest wave and current coexist widely in the ocean environments. However, the interaction between them has been studied recently and the method of velocity potential function was generally applied. Unlike the previous study, this article considers that location variable‘x'and time variable‘t'are independent of each other and it does not take into account the capillary effect, thus leading to an addition of a first-order time item in the second-order velocity potential function. Based on the perturbation technique, a second-order analytical solution is derived. Comparisons between the result in this article, where variables‘x'and‘t'are dependent on each other and the capillary effect is considered, and Huang's solutions show the difference. The difference between wave profile and wave pressure on mudline will become apparent with the increase of wave height, indicating that the solutions obtained in this article will be much suitable for ocean conditions with larger wave height.