Single-photon sources of high efficiency are of great interest because they are the key elements in many prospective quantum technologies and applications. Based on our previous work, here we demonstrate a high-quality tunable microwave single-photon source based on transmon qubit with intrinsic emission efficiency more than 99%. To further confirm the single-photon property of the source, we study the single-photon interference in a Hanbury-Brown-Twiss (HBT) type setup and measure the correlation functions of the emission field using linear detectors with GPU-enhanced signal processing technique. The antibunching in second-order correlation function is clearly observed. The theoretical calculations agree well with the experimental results. Such a high-quality single-photon source may be used as a building block for quantum communication, simulation and information processing in microwave regime.