The relevance of the work is caused by the extensive use of parametric linear programming problems in science, engineering, economics and the lack of effective methods to solve the researched class of problems. The main aim of the study is to develop an efficient algorithm for solving linear programming problems with parametric changes in coefficients of goal function and constraints, right-hand sides of constraints as well. The methods used in the study: the proposed method is based on G. E. Pukhov's differential transforms and simplex transformations for linear programming. Reverse transforms are performed by differential Pade restoring relations. The results: The paper introduces the solution of modeling example with parametric changes in coefficients of goal function and constraints, right-hand sides of constraints by below described method. The algorithm can be practically applied to various types of parametric programming problems both with linear and non-linear dependence on the parameters.