Strapdown Inertial Navigation System (SINS) and Doppler Velocity Log (DVL) are the main sensor devices for underwater navigation. The former can provide continuous autonomous navigation parameters but is limited by the gyroscope drift error in long-term operation, while the latter can accurately measure the velocity of the carrier, but in case of a long distance from the seafloor, the measured to-water velocity data does not represent the true motion of the carrier to the seafloor, and the resulting velocimetry error significantly affects the accuracy of underwater localization. In this paper, an integrated SINS/DVL navigation algorithm considering unknown currents velocity is proposed, which dynamically optimizes the observation equation and measurement matrix of Kalman filter according to whether the DVL is operating in water observation mode or not, effectively controlling the DVL velocimetry error due to the effect of the ocean currents and estimating the current velocity in real-time, simultaneously. The simulation and measurement data show that after applying this method, the horizontal position error of underwater navigation is significantly reduced, and the current velocity estimation achieves high accuracy, with the upper limit of the error being only 0.02 m/s. It verifies that the integrated navigation method of SINS/DVL considering unknown current velocity influence has important theoretical significance and practical application potential for improving the high-precision navigation performance of the underwater vehicle under the complex ocean current environment.