Grant-free transmission is considered as a promising technology to support sporadic data transmission in massive machine-type communications (mMTC). Due to the distributed manner, high collision probability is an inherent drawback of grant-free access techniques. Non-orthogonal multiple access (NOMA) is expected to be used in uplink grant-free transmission, multiplying connection opportunities by exploiting power domain resources. However, it is usually applied for coordinated transmissions where the base station performs coordination with full channel state information, which is not suitable for grant-free techniques. In this paper, we propose a novel distributed layered grant-free NOMA framework. Under this framework, we divide the cell into different layers based on predetermined inter-layer received power difference. A distributed layered grant-free NOMA based hybrid transmission scheme is proposed to reduce collision probability. Moreover, we derive the closed-form expression of connection throughput. A joint access control and NOMA layer selection (JACNLS) algorithm is proposed to solve the connection throughput optimization problem. The numerical and simulation results reveal that, when the system is overloaded, our proposed scheme outperforms the grant-free-only scheme by three orders of magnitude in terms of expected connection throughput and outperforms coordinated OMA transmission schemes by 31.25\% with only 0.0189\% signaling overhead of the latter.