We present a local convergence analysis of the proximal Gauss-Newton method for solving penalized nonlinear least squares problems in a Hilbert space setting. Using more precise majorant conditions than in earlier studies such as (Allende and Goncalves) [1], (Ferreira et al., 2011) [9] and a combination of a majorant and a center majorant function, we provide: a larger radius of convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost as in earlier studies using only the majorant function. (C) 2014 Elsevier Inc. All rights reserved.