A new adaptive control approach is proposed to deal with nonlinear systems with a class of time-varying parametric uncertainties, which are in an unknown compact set, periodic, nonvanishing, rapid time-varying, and the only prior knowledge is the periodicity. Unlike most continuous time adaptation laws which are of differential types, in this work a periodic type adaptation law is introduced for continuous time systems. The new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period, in the sequel achieves the asymptotic tracking convergence.