This paper addresses the position and attitude tracking control problem for a recently designed ellipsoidal airship with four vectored thrusters. External disturbances, thruster faults, mass matrix and aerodynamic coefficient uncertainties, which are inevitably encountered in practice, can deteriorate the control system performance of airship and even lead to system instability. To meet these challenges, we develop an adaptive integral sliding mode control method without requiring the prior knowledge of mass matrix and aerodynamic coefficients, in which these uncertainties and faults are considered simultaneously. We showed that the three Cartesian positions and three Euler attitude angles could globally asymptotically track the desired values in the face of external disturbances, thruster faults, mass matrix and aerodynamic coefficient uncertainties. Simulation results validate the effectiveness and advantage of proposed methods.