The shock layer problem, described by the second order linear differential equation, with the single turning point is considered. The solution is presented as a sum of the left and right reduced solution and the layer function, which is approximated by the truncated Jacobi orthogonal series. The layer subinterval is determined through the numerical layer length, which depends on the perturbation parameter and the degree of the spectral approximation. The coefficients in the differential equation are approximated by the appropriate power series and certain recurrence relations between the coefficients in the Jacobi orthogonal series are presented. The upper bound for the error function is constructed and the numerical example is included.