In this paper, it investigates the uplink performance of cell-free massive multiple-input multiple-output with non-orthogonal multiple access (CF-mMIMO-NOMA) technique and derives a rigorous closed-form approximation of the spectral efficiency expression for conjugate beamforming receiver. Based on this novel closed-form result, this paper proposes a total spectral efficiency maximization algorithm, subjecting to each user's quality-of-service (QoS) constraint, transmission power constraint, and successive interference cancellation (SIC) constraint. The original problem is non-convex, and hence, the sequential convex approximation (SCA) method is utilized in this paper and converts this issue into an iterative geometric programming (GP) problem. Simulation results demonstrate that CF-mMIMO-NOMA is able to exploit the scarce spectrum bands more efficiently than the orthogonal multiple access (OMA) counterpart. Furthermore, the proposed algorithm has a faster convergence rate and is able to significantly improve the total spectral efficiency, compared with the equal power control (EPC) scheme.