Summary: A boundary value problem for a linear second-order ordinary differential equation with small parameters by first and the second derivatives is considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form an exponentially fitted difference scheme on a uniform mesh is developed which is shown to be \(\varepsilon\)-uniformly first-order accurate in the \(C(\overline \omega_h)\) norm for original problem. Numerical results are also given.