We report on the tunable edge-plasmon-enhanced absorption of phosphorene nanoribbons supported on a dielectric substrate. Monolayer anisotropic black phosphorous (phosphorene) nanoribbons are explored for light trapping and absorption enhancement on different dielectric substrates. We show that these phosphorene ribbons support infrared surface plasmons with high spatial confinement. The peak position and bandwidth of the calculated phosphorene absorption spectra are tunable with low loss over a wide wavelength range via the surrounding dielectric environment of the periodic nanoribbons. Simulation results show strong edge plasmon modes and enhanced absorption as well as a red-shift of the peak resonance wavelength. The periodic Fabry-Perot grating model was used to analytically evaluate the absorption resonance arising from the edge of the ribbons for comparison with the simulation. The results show promise for the promotion of phosphorene plasmons for both fundamental studies and potential applications in the infrared spectral range.