In this paper, a numerical simulation study of flow and heat transfer in a grooved channel consisting of ten rectangular grooves with steady and pulsating flow is carried out. Numerical simulations of the steady flow with small perturbations applied at Re = 800, 1200, 1600, and 2000 show that the same intrinsic frequency fN exists at different positions, amplitudes, and durations, and it disappears gradually with the development of the flow. A sinusoidal pulsating flow with different frequencies is applied to the grooved channel with the dimensionless amplitude A fixed at 0.2. The flow and heat transfer properties of the grooved channel are investigated in the case of pulsating inflow, and it is found that there exists a vortex periodic formation–development–convergence–dissipation process inside each groove. The results show that the increase in the time-averaged Nusselt number is 44.12%, 57.75%, 53.21%, 52.93%, the time-averaged friction factor is increased by 58.23%, 133.04%, 140.80%, 151.26%, and the PECs is decreased with the increase in Reynolds number to be 1.24, 1.19, 1.14, and 1.12, respectively, when compared with the constant flow. When the forcing frequency is equal to the hydrodynamic instability frequency, the time-averaged Nusselt number of the grooved channel will reach its maximum value. Also, the dynamic mode decomposition analysis shows that the pulsation mode energy is maximum when the forcing frequency is equal to the hydrodynamic instability frequency. It shows that the applied pulsating flow has a positive effect of enhanced heat transfer, and the positive effect decreases with the increase in Reynolds number.