Abstract: Sparse recovery using a measuring matrix with grid is a common way to estimate multipath sparse channel. Grid is the main source of error in this kind of methods. The drawbacks of these methods could be significant when the grid interval is large. A much more accurate estimating method is proposed in this paper employing the theory of continuous compressed sensing and LFM(linear frequency modulated) training sequence. This method abandons the dictionary and grid thus avoids the error that is caused by grid, so that it could estimate the multipath sparse channel with high accuracy and resolution. This paper describes the method theoretically and then testifies it in two different sparse channel models. Numerical simulation results illustrate that the proposed method could estimate the multipath sparse channel very accurately and it outperforms the conventional methods that are with grid.