Reliable and accurate estimation of aquifer parameters is a key process in efficiently managing the groundwater resources of a region. Today, a number of stochastic optimisation tools are available to solve the non-linear aquifer parameters using gradient-based techniques. However, these tools use conventional stabilisation techniques in estimating the non-linear parameters. In the present study, an attempt was made to accelerate and stabilise the conventional Levenberg-Marquardt algorithm. A generalised Matlab code was developed to estimate the transmissivity and storage coefficient of the confined aquifer by considering the residual drawdowns measured in a single observation well. The applicability of the present method was illustrated by considering two datasets from different sources and the results were compared with previous research. Statistical analysis on the estimated parameters demonstrated that the present method can estimate the confined aquifer parameters accurately with a more rapid convergence in comparison with the conventional algorithms.