Secure key rate (SKR) of point-point quantum key distribution (QKD) is fundamentally bounded by the rate-loss limit. Recent breakthrough of twin-field (TF) QKD can overcome this limit and enables long distance quantum communication, but its implementation necessitates complex global phase tracking and requires strong phase references that not only add to noise but also reduce the duty cycle for quantum transmission. Here, we resolve these shortcomings, and importantly achieve even higher SKRs than TF-QKD, via implementing an innovative but simpler measurement-device-independent QKD that realizes repeaterlike communication through asynchronous coincidence pairing. Over 413 and 508 km optical fibers, we achieve finite-size SKRs of 590.61 and 42.64 bit/s, which are respectively 1.80 and 4.08 times of their corresponding absolute rate limits. Significantly, the SKR at 306 km exceeds 5 kbit/s and meets the bitrate requirement for live one-time-pad encryption of voice communication. Our work will bring forward economical and efficient intercity quantum-secure networks.