The problem of the model-free adaptive resilient control (MFARC) for nonlinear cyber-physical systems (CPSs) suffered from aperiodic jamming attacks is investigated in this article. First, the MFARC framework subject to aperiodic jamming attacks is established, and an intermediate variable method is introduced to avoid using the unavailable time-varying parameter and further eliminate an extra assumption on the sign limit of it. Then, a MFARC scheme is devised to track the desired output, where the problem of the tracking control can be transformed into solving a feasibility problem, and the controller parameters can be obtained with the aid of the linear matrix inequality technique. What is more, a novel attack compensation mechanism is developed in the MFARC scheme to mitigate the impact of aperiodic jamming attacks. In the last, an example is provided to verify the effectiveness of the devised MFARC scheme.