<p>This paper aims to develop an efficient collocation technique utilizing the Taylor polynomials for solving nonlocal (three-point) third-order singular boundary value problems. The problem with nonlocal boundary conditions is transformed into an equivalent integral equation to avoid singularity at the origin and the approximation of various derivatives appearing in the original model. The integral equation is based on Green’s function, which varies for different values of the shape factor. Non-uniform collocation points are employed in the solution algorithm to transform the problem into a system of nonlinear algebraic equations, solvable by any iterative method. A detailed error analysis is provided for the designed algorithm. Some test examples are solved to demonstrate the effectiveness and robustness of the suggested method. It is worth noting that the numerical results are highly accurate for only a small number of collocation points.</p>