Partial differential equation (PDE)-constrained optimization, which involves optimizing a system subject to governing equations, is a key problem of modern science and engineering, with applications ranging from automobile designs and financial modeling to material science. However, solving such problems is computationally expensive on classical computers because it requires repeated, high-dimensional PDE simulations within an iterative optimization loop. While quantum algorithms for solving linear systems and PDEs have exhibited potential for quantum speedup, they often suffer from the “readout bottleneck”: extracting the full solution vector from a quantum state requires a prohibitive number of measurements. To circumvent this, several studies have focused on extracting some meaningful observables or using quantum PDE solvers as subroutines within larger quantum algorithms. In this work, we propose a fully coherent quantum algorithm for solving PDE-constrained optimiza- tion problems. Our primary contribution is the explicit construction of a quantum oracle for the objective function in the form of a block-encoding. This construction allows for the direct integration of a quantum PDE solver, which prepares the solution vector as a quantum state, with a quantum optimization algo- rithm that requires coherent access to the objective function. By maintaining the entire process within the quantum domain, our method eliminates the need for intermediate state tomography, thereby mitigating the readout overhead that typically hinders quantum PDE solvers. We provide a detailed mathematical framework for the block-encoding of objective functions defined by the solutions of PDEs. Furthermore, we numerically demonstrate the validity and robustness of our proposed method through two practical applications: (1) a parameter calibration problem in the Black-Scholes equation for financial derivatives, and (2) a material parameter design problem in the wave equation. Our results show that the proposed algorithm can accurately evaluate cost functions in a coherent manner.