  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
~ 2X10^{39} erg/s (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 ~ 3.6X10^{38} erg/s, 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 ~ 9X10^{37} erg/s), the spectrum is
harder again, and the source might be in the steep-powerlaw 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 HST images. In terms of the colors
and the luminosity, the counterpart is probably a G8 supergiant or a compact
red globular cluster containing ~2X10^5 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.
