In this paper, we explores a rapid imaging method based on a proposed random-like trajectory for compressed sensing (CS) which requires the sampling trajectory should satisfy the Restricted Isometry Property (RIP) condition. In the existing CS literature, the attentions are on randomly sampling points on the conventional trajectories. However, the proposed trajectory is a random-like trajectory generated based on the High Order Chirp (HOC) sequences, which use the Traveling Salesman Problem (TSP) solver to choose a "short" trajectory and design a time optimal gradient waveforms to satisfy the gradient amplitude and slew rate limitation. The MR physical feasibility of the proposed method is verified by the Bloch simulation, and the simulations show that the proposed method can reduce artifacts than conventional Spiral trajectory under the CS framework.