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The phase delay of a local electric field, being well-known in plasmonic nanostructures, has seldom been investigated to modulate the plasmon-exciton interaction. Here, with the single-particle spectroscopy method, we experimentally investigate the phase effect in plasmon-exciton coupling systems consisting of monolayer WSe2 and an individual gold nanorod. The local plasmon phase delay is tuned by adopting various nanorods with different resonant energies respective to the exciton. We find that the local plasmon phase delay between the excitons and the plasmonic modes is as equally essential as the amplitude. The phase delay modulates the plasmon-exciton coupling considerably, resulting in an asymmetric spectral line-shape due to the interference behavior. There is an excellent agreement for the phase delay between the numerically calculated near-field phase distribution and the experimental results. The local phase delay can act as an effective way to modulate the properties of plexcitonic coupling at the nanoscale, which may have potential applications in nanoscale sensing, solar energy devices, and enhancing nonlinear processes.