Firstly, a mathematical and physical derivation of the generalized instantaneous power theory is derived by using the circuit optimization method of conditional variation, thus gives a more generalized instantaneous power theory for multi-terminal circuit. Then, current and power decomposition method of the generalized instantaneous power theory is given from the point of view of the current detection in the paper. The current detection method based on the generalized instantaneous power theory is presented, and the block diagram of the current detection for multi-terminal circuit is also given. Finally, the current detection method is simulated by MATLAB, simulation results show the correctness of the current detection method based on the generalized instantaneous power theory. In addition, the current detection method based on the generalized instantaneous power theory can effectively avoid the coordinate transformation and the direct operation of the reactive power tensor, which can effectively reduce the hardware implementation.