Based on alternating direction multiplier method (ADMM), an inertial approximate relaxation alternating direction multiplier method (IPR-ADMM) was proposed to solve separable convex optimization feasible problems. The new algorithm not only integrated the advantages of inertia extrapolation term to improve the convergence of the algorithm, but also introduced random variables to accelerate the new step size randomly, so as to improve the flexibility of the algorithm. Under suitable assumptions, the global convergence of the algorithm was proved. The numerical results show that the larger the data dimension is, the faster and more stable the convergence of the algorithm is. Moreover, the convergence of IPR-ADMM algorithm is better than that of ePADM algorithm.