We present a multicolor multiphoton fluorescence microscope with single-photon counting sensitivity. The system integrates a standard multiphoton fluorescence microscope, an optical grating spectrograph operating in the UV-Vis wavelength region, and a 16-anode photomultiplier tube (PMT). The major technical innovation is in the development of a multichannel photon counting card (mC-PhCC) for direct signal collection from multi-anode PMTs. The electronic design of the mC-PhCC employs a high-throughput, fully-parallel, single-photon counting scheme along with a high-speed electrical or fiber-optical link interface to the data acquisition computer. There is no electronic crosstalk among the detection channels of the mC-PhCC. The collected signal remains linear up to an incident photon rate of 10(8) counts per second. The high-speed data interface offers ample bandwidth for real-time readout: 2 MByte lambda-stacks composed of 16 spectral channels, 256 x 256 pixel image with 12-bit dynamic range can be transferred at 30 frames per second. The modular design of the mC-PhCC can be readily extended to accommodate PMTs of more anodes. Data acquisition from a 64-anode PMT has been verified. As a demonstration of system performance, spectrally resolved images of fluorescent latex spheres and ex-vivo human skin are reported. The multicolor multiphoton microscope is suitable for highly sensitive, real-time, spectrally-resolved three-dimensional imaging in biomedical applications.