Mobile edge computing (MEC) is considered as a promising paradigm to extend the computation capability of smart mobile devices (SMDs) and reduce the task execution delay. In this paper, we formulate a stochastic optimization problem, which maximizes the system utility and ensures the queues stability subject to the power, subcarrier and computation resources constraints by the joint congestion control and resource allocation. Leveraging on the Lyapunov optimization technique, four subproblems are decomposed. Because the system utility maximization subproblem, congestion control subproblem and SMDs computation resource allocation subproblem are all single variable problems, we can obtain the solutions directly. The joint power and subcarrier allocation subproblem can be efficiently solved by utilizing alternating and time-sharing methods. By solving the four separate subproblems at each slot, we proposed a delay-aware task congestion control and resource allocation (DTCCRA) algorithm. Theoretical analysis shows that the system utility of proposed DTCCRA algorithm increases by 18.91% and 26.14% respectively compared with traditional average power allocation algorithm and average subcarrier allocation algorithm.