The spline collocations method given in [7] for solving boundary value problems without a singular perturbation is adapted for problems with singular perturbation. The exponential features of the exact solution are transferred to spline coefficients by "artifical viscousity". In this way a uniformly convergent method for solving problem: $\varepsilon y''+p(x)y'+q(x)y=f(x)$, $y'(0)-\alpha y(0)=\alpha_0$, $y(1)=\alpha_0$, $\alpha\geq0$, $p(x)>0$, $q(x)\equiv0$ is achieved. The numerical results indicate a uniform convergence when $q(x)\neq 0$.