There have been different approaches to compute the analytic instantaneous frequency with a variety of background reasoning and applicability in practice, as well as restrictions. This paper presents an adaptive Fourier decomposition and ( -counting) based instantaneous frequency computation approach. The adaptive Fourier decomposition is a recently proposed new signal decomposition approach. The instantaneous frequency can be computed through the so called mono-components decomposed by it. Due to the fast energy convergency, the highest frequency of the signal will be discarded by the adaptive Fourier decomposition, which represents the noise of the signal in most of the situation. A new instantaneous frequency definition for a large class of so-called simple waves is also proposed in this paper. Simple wave contains a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. The -counting instantaneous frequency can be used to compute the highest frequency for a signal. Combination of these two approaches one can obtain the IFs of the whole signal. An experiment is demonstrated the computation procedure with promising results.