Iterative methods for complex number linear systems arising in high-frequency electromagnetic field problems often exhibit slow convergence, largely because Krylov subspace methods for these problems are highly sensitive to rounding errors, which can significantly degrade their convergence behavior. Furthermore, as the problem scales up, the accumulation of rounding errors becomes more critical, further worsening the convergence of iterative solvers. Hence, there is a great demand for accelerating iterative methods. High precision calculation is effective for reducing the number of iterations. There are various mixed-precision iterative methods to reduce computation time. However, mixed-precision methods are more computationally expensive than double precision methods, and thus, usually fail to reduce the total computation time. This motivates us to propose a mixed-precision iterative solver that reduces both the number of iterations and the computation time. The proposed method aims to reduce the overall computation time for the COCG (Conjugate Orthogonal Conjugate Gradient) method. Our method enhances convergence by starting the computation with DD (double-double) precision. Once a certain criteria is satisfied during the computation of search vectors, the method switches to double precision to reduce computation time per iteration. This hybrid approach ensures stable convergence and reduces the total computation time compared to the conventional DD precision method. Furthermore, the proposed method minimizes memory overhead and reduces calculation time by storing the coefficient matrix and the preconditioning matrix in double precision format, even when performing calculations in DD precision. We performed some numerical experiments for matrices obtained from high frequency electromagnetic field problems. The proposed method successfully reduced the total computation time by up to 62% compared to the DD method while maintaining stable convergence. Remarkably, it even outperforms double precision solvers in some cases, achieving a further reduction in computation time of up to 8.7%. Numerical results demonstrate that the proposed method is both robust and computationally efficient. In future work, we will investigate the effectiveness of the proposed method for a wide range of problems.