The sparse mixture iterative closest point （SM-ICP） method is proposed for achieving accurate alignment of point-sets， while avoiding the influence of outliers. This study investigates sparse representation， non-convex optimization， and point-sets registration. First， the registered residuals are represented by mixed regularization to establish a sparse mixture formula. The alternating direction of multiplier method （ADMM） is then integrated to solve the proposed formula using a nested framework. Among the variables， the balance weight θ for mixed regularization can be calculated using a sigmoid function. The scalar version is also provided to represent the corresponding loss of function in the inner loop of ADMM. Finally， the soft threshold formula for the scalar version can be deduced in point-set registration. Experimental results indicate that the registration accuracy of the proposed SM-ICP method is better than the that of established algorithms investigated for comparison. This improved accuracy is especially striking in the registration experiment of the Stanford bunny dataset. With 50% overlap rate， the trimmed registration error of SM-ICP was 2.04×10^-4. Compared with other methods， our trimmed error was one order of magnitude lower than those of the robust Trimmed-ICP （robust Tr-ICP） and ICP algorithms. Moreover， it was approximately three times lower than the error obtained using the sparse ICP （S-ICP） algorithm. In the registration experiments for both other objects and for scene data， the registration accuracy of the SM-ICP method also performed better than comparable algorithms. In the registration experiment of point-sets with different levels of random noise， the trimmed registration error of SM-ICP was 4.90×10^-6~1.33×10^-4. This was several times to one order of magnitude lower than those of other algorithms. In the registration experiment for the engine blade， our method successfully achieved accurate registration of point-sets， but the results produced by comparable algorithms displayed different degrees of dislocation in their point-sets registration. In summary， the proposed SM-ICP algorithm displays advantages in accuracy， robustness， and generalization for point-set registration.