In this paper, the Mixed Discrete Least Squared Meshless (MDLSM) method is used for solving quadratic Partial Differential Equations (PDEs). In the MDLSM method, the domain is discretized only with nodes, and a minimization of a least squares functional is carried out. The least square functional is defined as the sum of the residuals of the governing differential equation and its boundary condition at the nodal points. In MDLSM, the main unknown parameter and its first derivatives are approximated independently with the same Moving Least Squares (MLS) shape functions. The solution of the quadratic PDE does not, therefore, require calculation of the complex second order derivatives of MLS shape functions. Furthermore, both Neumann and Dirichlet boundary conditions can be treated and imposed as a Dirichlet type boundary condition, which is applied using a penalty method. The accuracy and efficiency of the MDLSM method are tested against three numerical benchmark examples from one-dimensional and two-dimensional PDEs. The results are produced and compared with the irreducible DLSM method and exact analytical solutions, indicating the ability and efficiency of the MDLSM method in efficient and effective solution of quadratic PDEs.@en