Limited by the detection principle, an electromagnetic log (EML) can only output a velocity measurement relative to the ocean current in marine applications, which thus leads to a negative effect on a strapdown inertial navigation system (SINS)/EML integrated navigation system. The current velocity usually can be modeled as a first-order Gaussian Markov process, while the Markov time correlation constant should be determined in advance and used as a constant during the navigation process. The integrated navigation system will suffer performance degradation if an incorrect time correlation constant is applied. In order to tackle the problem, an ocean current coefficient estimation method is proposed in this manuscript. According to the Markov nature, the current velocity at the present time epoch is determined by that at the previous time epoch. Consequently, the current velocity corrected by the Kalman filter (KF) at the previous time epoch is utilized as the measurement information at the present time epoch, where the current coefficient is introduced into the state vector. The observability analysis shows that the current coefficient is totally observable. Simulation and field test results indicate that the proposed method can accurately estimate the current coefficient. Compared to the SINS/EML integrated navigation system without considering the current effects, the system with an estimated current coefficient minimizes the effect caused by ocean currents.