A cylindrical perfectly matched layer is developed based on the complex coordinate system approach. By an analytic continuation of the radial coordinate to complex values, the fields can be attenuated in the radial direction with no reflection (in the continuum space) for all angles of incidence and all frequencies. In the time domain the complex stretching leads to convolutions of the fields with the stretched space coordinates. These can be done quite efficiently by using recursive convolution. The accuracy of the formulation was validated by computing the field from a line source on a cylindrical grid and comparing the result against an analytic solution.