The strong secrecy transmission problem of arbitrarily varying wiretap channel (AVWC) with input and state constraints is investigated in this paper. A stochastic code lower bound of the secrecy capacity is established by applying the type argument and Csiszár's almost independent coloring lemma, which includes the result of the ordinary AVWC as special case. Our codebook generation without the i.i.d. assumption of the soft covering lemma is to ensure the reliable communication over the AVWC with constraints. It is proved that the 0good codebooks for the strong secrecy transmission can be generated by choosing codewords randomly from a given type set, which is critical in this model.