For multispectral image acquisition in remote sensing, high spatial resolution requires a small instantaneous field of view (IFOV). However, the smaller the IFOV, the lower the amount of light exposure to imaging sensors, and the lower the signal-to-noise ratio. To overcome this weakness, we propose a new random coded exposure technique for acquiring high-resolution multispectral images without reducing IFOV. The new image acquisition system employs a high-speed rotating mirror controlled by a random sequence to modulate exposure to an ordinary imager without increasing the sampling rate. The proposed high-speed coded exposure strategy makes it possible to maintain sufficient light exposure even with a small IFOV. The randomly sampled multispectral image can be recovered in high spatial resolution by exploiting the signal sparsity. The recovery algorithm is based on the compressive sensing theory. Simulation results demonstrate the efficacy of the proposed technique.