With the development of quantum technology, an arising researching point is to solve some new cipher problems with quantum technology to ensure their security. As we know, the sequential signature means to sign a contract or a document by many signers one by one. It has been widely used to realize layered authentication. In this paper, we propose a quantum sequential signature protocol with a set of strongly nonlocal orthogonal product (Y-SNOP) states. It is proved that the present protocol is secure, i.e., anyone cannot deny or forge a valid signature even some of them conspire. Compared with the existing quantum multi signature with some nonlocal orthogonal product (NOP) states, the present protocol seems more efficient and easier to be realized in Noisy Intermediate-Scale Quantum (NISQ) device as no entangled resources are required.INDEX TERMS Quantum sequential signature, strongly nonlocal orthogonal product, collusion attack.