In this research article, the non-linear shooting method is modified (MNLSM) and is considered to simulate Troesch’s sensitive problem (TSP) numerically. TSP is a 2nd order non-linear BVP with Dirichlet boundary conditions. In MNLSM, classical 4th order Runge-Kutta method is replaced by Adams-Bashforth-Moulton method, both for systems of ODEs. MNLSM showed to be efficient and is easy for implementation. Numerical results are given to show the performance of MNLSM, compared to the exact solution and to the results by He’s polynomials. Also, discussion of results and the comparison with other applied techniques from the literature are given for TSP.