We report the discovery of a new ultraluminous X-ray source (ULX) 2XMM J125048.6+410743 within the spiral galaxy M94. The source has been observed by ROSAT, Chandra, and XMM-Newton on several occasions, exhibiting as a highly variable persistent source or a recurrent transient with a flux variation factor of 100, a high duty cycle (at least ∼70%), and a peak luminosity of LX ∼ 2 × 1039 erg s−1 (0.2–10 keV, absorbed). In the brightest observation, the source is similar to typical low-luminosity ULXs, with the spectrum showing a high-energy cutoff but harder than that from a standard accretion disk. There are also sporadical short dips, accompanied by spectral softening. In a fainter observation with LX ∼ 3.6×1038 erg s−1, the source appears softer and is probably in the thermal state seen in Galactic black hole X-ray binaries (BHBs). In an even fainter observation (LX ∼ 9×1037 erg s−1), the spectrum is harder again, and the source might be in the steep-power-law state or the hard state of BHBs. In this observation, the light curve might exhibit ∼7 hr (quasi-)periodic large modulations over two cycles. The source also has a possible point-like optical counterpart from Hubble Space Telescope images. In terms of the colors and the luminosity, the counterpart is probably a G8 supergiant or a compact red globular cluster containing ∼2 × 105 K dwarfs, with some possible weak UV excess that might be ascribed to accretion activity. Thus, our source is a candidate stellar-mass BHB with a supergiant companion or with a dwarf companion residing in a globular cluster. Our study supports that some low-luminosity ULXs are supercritically accreting stellar-mass BHBs.