This paper investigates a general partial synchronization of drive-response Boolean networks with switching structure, where the total number of synchronized nodes is fixed but the anticipated nodes are not fixed. In addition, this general partial synchronization is an extension of common p-partial synchronization, where the p anticipated nodes are preliminary fixed. By defining a Hamming distance output system, the general partial synchronization issue is studied based on the semi-tensor product of matrix. Further, a necessary and sufficient criterion for the general partial synchronization is obtained. The obtained results are effectively illustrated by numerical example.