We address reducing the mismatch between training and testing conditions for hands-free in-car speech recognition. It is well known that the distortions caused by background noise, channel effects, etc., are highly nonlinear in the log-spectral or cepstral domain. This letter introduces a joint sparse representation (JSR) to estimate the underlying clean feature vector from a noisy feature vector. Performing a joint dictionary learning by sharing the same representation coefficients, the proposed method intends to capture the complex relationships (or mapping functions) between clean and noisy speech. Speech recognition experiments on realistic in-car data demonstrate that the proposed method shows excellent recognition performance with a relative improvement of 39.4% compared with the 'baseline' frontends.