In quantum mechanics,the expectation value of an operator can be measured by using the projective measurement,if the coupling between the measured system and pointer is strong enough.However in the weak coupling regime,the pointer can not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states,which makes the measurement of the expectation value difficult.In this paper,we propose an expectation value measurement method in the weak coupling regime inspired by the weak measurement scheme.Compared to the projective measurement,our scheme has two obvious advantages.Experimentally we use the internal state and motional state of a single trapped 40Ca+to establish the measurement scheme and realize the proof of principle demonstration of the scheme.