As quantum computation advances, stable and cost-effective quantum communication remains a significant challenge. This has led to the emergence of the Quantum-Computation Classical-Communication (QCCC) model, a practically motivated framework where parties perform local quantum computations but communicate exclusively through classical channels. Despite substantial progress in quantum commitment schemes, prior constructions have either depended on quantum channels or relied on strong assumptions, such as collapsing hash functions. This raises the open question of whether collapse-binding commitments can be achieved in the QCCC setting under weaker assumptions. In this work, we resolve this gap by constructing a constant-round QCCC commitment that is statistically hiding and computationally collapse-binding. Our approach adapts and extends the framework of Bitansky et al. [EUROCRYPT ’19]: structurally, we preserve their proof strategy while modifying it to operate in the QCCC model, and foundationally, we show that collapse-binding can be obtained from the average-case hardness of problems in \(\mathcal {SZK}\) . This both broadens the applicability of their techniques and improves upon prior work by avoiding reliance on collapsing hash functions.