We propose a novel method to sequentially optimize arbitrary single-qubit gates in parameterized quantum circuits for simulating real and imaginary time evolution. Unlike previously-known methods, the proposed method fully utilizes all parameters of single-qubit gates and therefore can potentially obtain better performance. Specifically, the proposed method simultaneously optimizes both the axis and the angle of a single-qubit gate. Furthermore, we demonstrate how the proposed method can be extended to optimize a set of parameterized two-qubit gates with excitation-conservation constraints. We perform numerical experiments showing the power of the proposed method to find ground states of typical Hamiltonians with quantum imaginary time evolution using parameterized quantum circuits.