With the development of multi-autonomous underwater vehicle(AUV) cooperative systems, the evaluation of their reliability is becoming more and more important. Since AUVs are always in motion, the reliability of the system is not stationary, but it varies with time. This paper studies the time-varying reliability evaluation indexes for multi-AUV cooperative systems. Aimed at elucidating the characteristics of the system, by considering the motion of the AUVs, two time dependent reliability evaluation indexes, natural connectivity and all-terminal reliability of the basic reliability indexes, are determined with the graph theory. Then the timevarying reliability of multi-AUV cooperative systems is evaluated combining with an actual example. This paper provides a method to evaluate the time-varying reliability of multi-AUV cooperative systems. With the development of multi-autonomous underwater vehicle (AUV) cooperative systems, the evaluation of their reliability is becoming more and more important. Since AUVs are always in motion, the reliability of the system is not stationary, but it varies with time. This paper studies the time-varying reliability evaluation indexes for multi-AUV cooperative systems. Aimed at elucidating the characteristics of the system, by considering the motion of the AUVs, two time dependent reliability evaluation indexes, natural connectivity and all-terminal reliability of the basic Then the timevarying reliability of multi-AUV cooperative systems is evaluated combining with an actual example. This paper provides a method to evaluate the time-varying reliability of multi-AUV cooperative systems.