Miniaturization is one of the important research directions of low frequency high power microwave sources. This paper presents a three-period coaxial slow-wave structure L-band high-power microwave source. Because the coaxial Quasi-TEM mode has no cut-off frequency, the radial size of the device can be reduced. At the same time, in order to reduce the transverse dimension, the coaxial extractor structure is introduced to realize the longitudinal mode selection and improve the conversion efficiency of the device. In simulation, the device obtains the microwave output with the central frequency of 1.53 GHz, the average power of 3.3 GW and the efficiency of 40%. By optimizing the scheme of electron beam collection, the phenomenon of pulse shortening is effectively suppressed. In the experiment, the device obtains the microwave output with the central frequency of 1.52 GHz, the average power of 3 GW, the efficiency of 33% and the pulse width of 40 ns.