As an important part of the inertial device in the ship strap-down inertial attitude measurement and navigation system, the high reliability of fiber optic gyroscopes (FOGs) is significant for the long-term precision of navigation systems and mission success for ships. Due to the combined impact of the external service environment and internal physical field, the performance of FOGs will gradually degrade. Although many studies are dedicated to the degradation analysis and reliability assessment of FOGs, few have considered the 3-axis dependent degradation processes of FOGs simultaneously. Confronted with this problem and taking the scale factor and zero bias as two main degradation characteristics of the FOGs, this paper develops the degradation path model for each marginal degradation process on each of x, y and z axis. The unknown model parameters are estimated by maximum likelihood estimation method based on accelerated degradation test data. Furthermore, considering the dependence between the two marginal degradation processes on each axis, the reliability of the FOGs is evaluated by adapting the Gaussian copula function. It can be illustrated that the proposed degradation model and reliability assessment method are effective for FOGs and other products with 3-axis dependent degradation processes.