A diode-laser pumped blue intracavity frequency-doubled self-Q-switched microchip laser of a chromium Cr4+ Neodymium Nd3+ codoped yttrium aluminum garnet crystal (Cr4+Nd3+:YAG) combined with a potassium niobate (KNbO3) crystal is developed. By coating the cavity mirrors with the films that suppress the 1064-nm operation and enhance the 946-nm laser, the 4F3/24I9/2 transition of the Nd3+ ion is facilitated to achieve the 946-nm laser oscillation. The 946-nm laser of the Cr4+Nd3+:YAG is self-Q-switched due to the saturable absorption of the Cr4+ ion. The full width at half maximum (FWHM) of the laser pulse at a 964-nm wavelength is about 5.07 ns. A self-Q-switched 473-nm laser pulse is sequentially obtained through intracavity frequency doubling of the 946-nm laser by the KNbO3 crystal, whose FWHM is about 4.30 ns. The 473-nm intracavity doubled laser has a good fundamental transverse TEM00 mode, because the self-Q-switched 946-nm laser has a good TEM00 mode that results from the absorption bleaching established by both the 808-nm pump laser and 946-nm oscillating laser. The constant FWHM results from both the response time of the self-Q-switching and the establishing time of the oscillating laser being much faster than the accumulated time of the pump laser energy. The constant peak power of the 946-nm self-Q-switched laser mainly depends on the modulation ability of the self-Q-switching.