As a viable supplement to the fifth generation wireless communication, visible light communications (VLC) with affluent spectrum resources can cater to the ever-increasing high speed data transmission demand. However, the nonlinear characteristics of light emitting diode (LED) can distort the transmitted signal in the VLC link, which damages the communication quality. To mitigate the nonlinear impairments, a reproducing kernel Hilbert space post-distortion scheme is proposed in this paper, which is based on kernel recursive least squares (KRLS) with adaptive kernel width. In this kernel based method, the kernel width will affect the approximation ability of the model. Therefore, in the recursive process of KRLS, Gauss-Newton (GN) algorithm is adopted to update the kernel width. In addition, combined with the enhanced novelty criterion (ENC), the KRLS-GN post-distorter learns the sparse dictionary adaptively according to the input data, which is beneficial to complete the linearization under the limited memory budget constraints. The performance of the proposed KRLS-GN-ENC scheme is verified by simulations, and the results show that KRLS-GN-ENC can achieve a significant improvement over KRLS-ENC. Compared with the schemes based on classical polynomial filtering, KRLS-GN-ENC exhibits better nonlinear compensation performance and faster convergence speed.