We demonstrate a nanosecond pulsed source at 620 nm with watt-level average power by frequency-doubling a 1240 nm phosphosilicate Raman fiber amplifier. A gain-switched laser diode operating at 1064 nm is amplified in an ytterbium fiber master oscillator power amplifier system and then converted to 1240 nm using a phosphosilicate Raman fiber amplifier with a conversion efficiency of up to 66%. The Raman fiber amplifier is seeded with a continuous-wave 1240 nm laser diode to obtain narrow-linewidth radiation, which is subsequently frequency-doubled in a periodically poled lithium tantalate crystal. A maximum average power of 1.5 W is generated at 620 nm, corresponding to a pulse energy of 300 nJ at a repetition rate of 5 MHz. The source has excellent beam quality (M2≤1.16) and an optical efficiency (1064 nm to 620 nm) of 20%, demonstrating an effective architecture for generating red pulsed light for biomedical imaging applications.