To support massive Machine Type Communications (mMTC) applications, especially for overcoming the high overhead problem, compressive sensing algorithm for grantfree multiple access is advocated. For an mMTC system with a large number of users, in most existing research, each user is allocated a complex Gaussian random sequence, and approximated message passing (AMP) algorithm is normally employed at the receiver to detect the active users. In this paper, binary deterministic sequences are considered, resulting much simpler implementation. It is shown that, due to the smaller coherence value, significant performance gain can be obtained by employing the binary deterministic sequences into AMP process. In particular, binary quasi-orthogonal sequences (QOS) exhibit excellent performance in the short-packet transmission. Moreover, an improved AMP algorithm is presented by designing a new stopping criterion to reduce the number of iterations without loss of accuracy.