Projective measurement of single-electron spins, or spin readout, is among the most fundamental technologies for spin-based quantum information processing. Implementing spin readout with both high-fidelity and scalability is indispensable for developing fault-tolerant quantum computers in large-scale spin-qubit arrays. To achieve high fidelity, a latching mechanism is useful. However, the fidelity can be decreased by spin relaxation and charge state leakage, and the scalability is currently challenging. Here, we propose and demonstrate a double-latching high-fidelity spin readout scheme, which suppresses errors via an additional latching process. We experimentally show that the double-latching mechanism provides significantly higher fidelity than the conventional latching mechanism and estimate a potential spin readout fidelity of 99.94% using highly spin-dependent tunnel rates. Due to isolation from error-inducing processes, the double-latching mechanism combined with scalable charge readout is expected to be useful for large-scale spin-qubit arrays while maintaining high fidelity.