High-resolution compressive imaging via a flexible multimode fiber is demonstrated using a swept-laser source and wavelength dependent speckle illumination. An in-house built swept-source allowing for independent control of bandwidth and scanning range is used to explore and demonstrate a mechanically scan-free approach for high-resolution imaging through an ultrathin and flexible fiber probe. The computational image reconstruction is shown by utilizing a narrow sweeping bandwidth of <10 nm while acquisition time is decreased by 95% compared to conventional raster scanning endoscopy. Demonstrated narrow-band illumination in the visible spectrum is vital for the detection of fluorescence biomarkers in neuroimaging applications. The proposed approach yields device simplicity and flexibility for minimally invasive endoscopy.