Several short-lived radionuclides (SLRs) were present in the early solar system, some of which should have formed just prior to or soon after the solar system formation. Stellar nucleosynthesis has been proposed as the mechanism for production of SLRs in the solar system, but no appropriate stellar source has been found to explain the abundances of all solar system SLRs. In this study, we propose a faint supernova with mixing and fallback as a stellar source of SLRs with mean lives of <5 Myr (26Al, 41Ca, 53Mn, and 60Fe) in the solar system. In such a supernova, the inner region of the exploding star experiences mixing, a small fraction of mixed materials is ejected, and the rest undergoes fallback onto the core. The modeled SLR abundances agree well with their solar system abundances if mixing-fallback occurs within the C/O-burning layer. In some cases, the initial solar system abundances of the SLRs can be reproduced within a factor of 2. The dilution factor of supernova ejecta to the solar system materials is ~10E-4 and the time interval between the supernova explosion and the formation of oldest solid materials in the solar system is ~1 Myr. If the dilution occurred due to spherically symmetric expansion, a faint supernova should have occurred nearby the solar system forming region in a star cluster.
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