The third-order polynomial normal transformation（TPNT） technique was employed to transform a multivariate non-normal dependent random variables group into a multivariate standard normal independent one. Sampling points were obtained in the standard normal independent variable space and transformed into multivariate non-normal dependent ones. Incorporating three-point estimate method with TPNT technique， a TPNT-based three-point estimate method is proposed to solve probabilistic power flow problems with non-normal dependent variables. A case study on a slightly modified IEEE 118-bus system shows that， the proposed method has high accuracy and computational efficiency. It is a qualified tool to discuss the probabilistic power flow problems with non-normal dependent variables.