This paper describes the estimation of hydrodynamic coefficients and the control algorithm based on a nonlinear mathematical modeling for a test bed autonomous underwater vehicle (AUV) named by SNUUV I (Seoul National University Underwater Vehicle I). A six degree of freedom mathematical model for SNUUV I is derived with linear and nonlinear hydrodynamic coefficients, which are estimated with the help of a potential code and also the system identification using multi-variable regression. A navigation algorithm is developed using three ranging sonars, pressure sensor and two inclinometers keeping towing tank applications in mind. Based on the mathematical model, a simulation program using a model-based control algorithm is designed for heading control and wall following control of SNUUV I. It is demonstrated numerically that the navigation system together with controller guides the vehicle to follow the desired heading and path with a sufficient accuracy. Therefore the model-based control algorithm can be designed efficiently using the system identification method based on vehicle motion experiments with the appropriate navigation system.