REBa 2 Cu 3 O 7−δ coated conductors (REBCO-CCs; RE: rare-earth element or Y) have garnered considerable attention in high-field magnet applications. However, the twin structure existing in the ab plane of REBCO complicates the dependence of critical current density on temperature, magnetic field, and uniaxial strain: J c (T, B, ε). In particular, the mechanism for the appearance of anomalous double-peak structure in J c (T, B, ε) is unclear.In this study, to understand the complicated strain dependence of critical current density, we measured J c (77.3 K, B, ε) of REBCO-CCs with c-axis-correlated pins or with random pins as a function of in-plane uniaxial strain and magnetic field applied parallel to the c axis. In the case of (Y,Gd)BCO-CC with BaZrO 3 nanorods, we only observed a mountain-shaped response of J c (77.3 K, B, ε) under the entire magnetic field. However, GdBCO-CC without artificial pinning centers, where random pinning is dominant, exhibited a valley-shaped response at low fields and then a mountain-shaped response at high fields. These results suggest that the variation in the pinning mechanism (correlated-or random pins) plays a crucial role in the absence/presence of double-peak structure in REBCO-CCs.We developed a phenomenological model for J c (T, B, ε) in which (i) strain dependence of superconducting properties in two domains of REBCO and (ii) ideal behavior of correlated-or random pinning are considered. Consequently, we observed that the valley-shaped response of J c (T, B, ε) can be realized in the case of ideal random pinning with limited parameters, while ideal correlated pinning always exhibits a mountain-shaped response of J c (T, B, ε). Furthermore, a crossover from a valley-shaped response under low fields to a mountain-shaped response under high fields in the strain dependence of J c (T, B, ε) is qualitatively consistent with our observations. This qualitative agreement between our model and experimental data validates the efficacy of our model to provide a clear understanding of the strain dependence of J c (T, B, ε) in REBCO-CCs, including the anomalous double-peak structure.