The modified improved interpolating moving least squares (MIIMLS) method for meshless approaches has been developed. In a meshless method, the approximation accuracy of the derivative is directly proportional to the simulation accuracy. For improving the approximation accuracy of a derivative, we propose MIIMLS using Chebyshev nodes. In the approximation of a function, the results of MIIMLS reach the precision limit. In the approximation of a derivative, the MIIMLS method has high approximation accuracy between the nodes as compared to the conventional methods.