A nanosecond pulsed power source based on stacked Blumlein line is designed, consisting of four stages of plate Blumlein line, and each line with a GaAs Photoconductive Semiconductor Switches(PCSS). The Blumlein line is based on high-density polyethylene for energy storage. Its pulse width, impedance and total impedance are 2.5 ns, 25Ω, and 100Ω respectively. A Pspice model of the pulsed power source is established. Simulation results indicate that output voltage is affected by isolation resistance of the charging circuit, closed resistance and transition time of GaAs switch. Nanoseconds laser triggering experiments are tested, and the output waveforms are close to square waves with 38 kV of voltage, 1.4 ns of rising edge under 25 kV of charging voltage.