The estimation accuracy of the subspace algorithm has dropped off because the effective bandwidth has reduced under the condition of single snapshot. The accuracy of the compressed sensing algorithm has declined because of the similar sparse structure under the condition of multiple snapshots. To deal with the weak robustness of existing algorithms，a high-performance time delay estimation algorithm is presented based on compressed sensing subspace under both conditions. The proposed algorithm derives the relationship between the multipath number and the number of snapshots. An improved noise subspace has been reconstructed. The polynomial is applied to estimate time delay. The polynomial rooting avoids the spectral peak searching and reduces the computational complexity. Simulation results show that the proposed algorithm has a high performance and a better robustness compared with subspace algorithms and compressed sensing algorithms.