Massive machine-type communication (mMTC) has been identified as one of the three generic 5G services, with the aim of providing connectivity to a large number of devices. The concurrent massive access may lead to congestions due to limited access resources. Group paging (GP) has emerged as one of the promising solutions to alleviate network congestion by controlling access load. However, the performance of GP deteriorates drastically with the number of devices per paging group. This paper explores GP with pre-backoff strategy for a general mMTC scenario in which devices are allowed to have diverse access success probability (ASP) requirements, and proposes an ASP requirement guaranteed GP scheme with specific pre-backoff times (GPSP), with the aim of maximizing the total access rate. To fully adapt to mMTC applications, an efficient heuristic algorithm is designed. Numerical results demonstrate that the proposed GPSP scheme can effectively improve system performance in terms of average ASP, average access delay, and the average number of preamble transmissions.