Composite multilayer films (CMLs) comprising YBa 2 Cu 3 O 7 +BaHfO 3 (4.7 vol%)/YBa 2 Cu 3 O 7 +BaHfO 3 (3.1 vol%) were fabricated, and vortex behavior in the CMLs was evaluated to discuss inhomogeneous depinning of vortices. Magnetic field and angular dependences of critical current density (J c ) in the CMLs were similar to those in the YBa 2 Cu 3 O 7 +BaHfO 3 (4.7 vol%) single layer film (SL). Variation of the CML structure shifted the matching field effect in global pinning force and irreversibility temperature. The J c in the YBa 2 Cu 3 O 7 +BaHfO 3 (4.7 vol%) SL was smaller than that in the YBa 2 Cu 3 O 7 +BaHfO 3 (3.1 vol%) SL, suggesting that vortices preferentially moved along the low-J c layers in the CMLs. The high-J c layers pinned the vortices in the low-J c layers, resulting in a shift of the matching field effect. These observations are characteristic of inhomogeneous depinning of vortices in the CMLs. The inhomogeneous depinning as well as pinned configuration should be considered for understanding J c and for structural design of pinning centers in YBa 2 Cu 3 O 7 films.