The accurate estimation of shallow subsurface velocity models with complex topography is crucial for statics corrections and imaging deep structures. The correlation-based wave-equation traveltime inversion (CWTI) method is suitable for estimating such shallow subsurface velocity structures. However, the CWTI objective function suffers an inherent resolution-loss problem since the traveltime weighted crosscorrelation misfit does not fall to zero even when the model is perfectly matched. Furthermore, the Born-approximation-based CWTI gradient cannot provide an effective model update during each iteration. To overcome these problems, we propose a least-squares correlation-based full traveltime inversion (LCFTI) method in which the least-squares correlation-based objective function is designed to minimize the traveltime weighted difference between the autocorrelation and the crosscorrelation. By incorporating the autocorrelation, LCFTI shows better convergence and higher resolution than CWTI. The LCFTI model updates are derived using the Rytov approximation to avoid incorrect model updates by emphasizing phase matching. Furthermore, to accurately simulate wave propagation, we use the spectral-element method as the modeling engine in which the mesh of the complex topography is flexibly represented. Synthetic and field data examples are shown to demonstrate the effectiveness of the proposed method in shallow subsurface velocity reconstruction.