This paper proposes an effective continuous super-resolution (CSR) algorithm for the multipath channel estimation. By designing a preamble including up-chirp and down-chirp symbols, the Doppler shift and multipath delay are estimated jointly by using convex programming. Simulation results show that the proposed CSR can achieve better detection probability of the number of multipaths than the eigenvalue based methods. Moreover, compared with conventional super-resolution techniques, such as MUSIC and ESPRIT methods, the proposed CSR algorithm demonstrates its advantage in root mean square error of the Doppler shift and multipath delay, especially for the closely located paths within low SNR.