An important aspect for the task of grammatical error correction (GEC) that has not yet been adequately explored is adaptation based on the native language (L1) of writers, despite the marked influences of L1 on second language (L2) writing. In this paper, we adapt a neural network joint model (NNJM) using L1-specific learner text and integrate it into a statistical machine translation (SMT) based GEC system. Specifically, we train an NNJM on general learner text (not L1-specific) and subsequently train on L1-specific data using a Kullback-Leibler divergence regularized objective function in order to preserve generalization of the model. We incorporate this adapted NNJM as a feature in an SMT-based English GEC system and show that adaptation achieves significant F0.5 score gains on English texts written by L1 Chinese, Russian, and Spanish writers.