Chromium telluride Cr3Te4 with intrinsic room-temperature ferromagnetism has substantially practical application in spintronics. In this work, the microwave response of Cr3Te4 single crystal is investigated by the electronic spin resonance (ESR) with the magnetic field applied along various directions. Two resonance lines are observed for both H//ab and H//c, which are suggested to result from ferromagnetic (FM) and antiferromagnetic (AFM) fluctuations respectively. The angle-dependent ESR spectra show considerable anisotropy, with a strong microwave response for H//ab and a weak microwave response for H//c. The analysis of the ESR spectra reveals the coexistence of FM and AFM fluctuations in this system. Moreover, this anisotropic microwave response in single crystal Cr3Te4 could benefit the microwave-based spintronic device.