<p>This paper presents an innovative and efficient numerical method for solving nonlinear singular two-point boundary value problems (BVPs) with logarithmic singularities. The method combines the logarithmic singular Puiseux series asymptotic technique with an augmented compact finite volume method (FVM) to achieve high-order accuracy in solving these problems. The core of the method is to express the solution as the Puiseux series expansion involving logarithmic factors near the singularity. The expansion contains an undetermined parameter, which is the augmented variable in the compact FVM on the regular subinterval. In this way, a nonlinear system of equations is constructed to obtain the parameter and the numerical solution simultaneously. The paper also provides an error analysis of the hybrid method, demonstrating that the compact FVM attains fourth-order accuracy. Numerical experiments are provided to validate the theoretical results and confirm the effectiveness of this novel approach for solving singular differential equations with logarithmic singularities.</p>