With the ability of revealing the interactions between objects and electromagnetic waves, hyperspectral imaging in optical microscopy is of great importance in the study of various micro/nano-scale physical and chemical phenomena. The conventional methods, however, require various scanning processes to acquire a complete set of hyperspectral data because of its 3-dimensional structure. As such the quality and efficiency of the data acquisition using these conventional scanning techniques is greatly limited by the detector sensitivity and low signal light intensity from the sample. To overcome such limitations, we applied compressive sensing theory to the hyperspectral imaging. The compressive imaging enhances the measurement signal-to-noise ratio by encoding and combining the spatial information of the sample to the detector, and a recovery algorithm is used to decode the detector outputs and reconstruct the image. A microscopy system based on this compressive hyperspectral imaging scheme was designed and implemented. Further analysis and discussion on the diffraction and interference phenomenon and a solution to the spectral distortion in this compressive sensing microscopy system are also presented. Experimental results of compressive dark-field scattering from gold nanobelts are presented, followed with an analysis on signal-to-noise ratio and a comparison with conventional scanning methods in measuring the plasmon resonances.