Swimming is a kind of complex locomotion that involves the interaction between the human body and the water. Here, to examine the effects of currents on the performance of freestyle and breaststroke swimming, a multi-body Newton-Euler dynamic model of human swimming is developed. The model consists of 18 rigid segments, whose shapes and geometries are determined based on the measured data from 3D scanning, and the fluid drags in consideration of the current are modeled. By establishing the interrelations between the fluid moments and the swimming kinematics, the underlying mechanism that triggers the turning of the human body is uncovered. Through systematic parametric analyses, the effects of currents on swimming performance (including the human body orientation, swimming direction, swimming speed, and propulsive efficiency) are elucidated. It reveals that the current would turn the human body counterclockwise in freestyle swimming, while clockwise in breaststroke swimming (which means that from the top view, the human trunk, i.e., the vector pointing from the bottom of feet to the top of the head, rotates counterclockwise or clockwise). Moreover, for both strokes, there exists a critical current condition, beyond which, the absolute swimming direction will be reversed. This work provides a wealth of fundamental insights into the swimming dynamics in the presence of currents, and the proposed modeling and analysis framework is promising to be used for analyzing the human swimming behavior in open water.