Massive machine-type communications (mMTC) is envisioned to be one of the pivotal scenarios in the fifth-generation (5G) wireless communication, where the explosively emerging Internet-of-Things (IoT) applications have triggered the demand for services with low-latency and high-reliability. To this end, grant-free random access paradigm has been proposed as a promising enabler in simplifying the connection procedure and significantly reducing access latency. In this paper, we propose to leverage the burgeoning reconfigurable intelligent surface (RIS) for grant-free massive access working at millimeter-wave (mmWave) frequency to further boost access reliability. By attaching independently controllable phase shifts, reconfiguring, and refracting the propagation of incident electromagnetic waves, the deployed RISs could provide additional diversity gain and enhance the access channel conditions. On this basis, to address the challenging active device detection (ADD) and channel estimation (CE) problem, we develop a joint-ADDCE (JADDCE) method by resorting to the existing approximate message passing (AMP) algorithm with expectation maximization (EM) to extract the structured common sparsity in traffic behaviors and cascaded channel matrices. Finally, simulations are carried out to demonstrate the superiority of our proposed scheme.