A single valued neutrosophic number ($$S_{VN}$$ number) is one type of neutrosophic set defined over the set of real numbers. This $$S_{VN}$$ number is here used to extend the concept of crisp linear programming problem ($$L_P$$-problem) in neutrosophic environment. The coefficients in objective function, technical coefficients, right hand side coefficients and decision variables of an $$L_P$$-problem are considered as $$S_{VN}$$ numbers. This kind of $$L_P$$-problem is called a neutrosophic linear programming problem ($$N_{LP}$$ problem). An attempt has been made to solve such problems by Big-M simplex method. An algorithm of Big-M simplex method is proposed in this new climate. Then it is applied to a real life problem.