This paper proposes a method for stable bipedal walking with a vertical center-of-mass (COM) motion by an evolutionary optimized central pattern generator (CPG). To generate a walking pattern for a bipedal robot, a modifiable walking pattern generator (MWPG) is employed, which extends a conventional 3-D linear inverted pendulum model (3-D LIPM) to allow a zero-moment-point variation by the closed-form functions. By using the MWPG, the robot is able to modify the walking pattern in real time while walking. For the vertical COM motion of the 3-D LIPM, the vertical COM trajectory is generated by the CPG. The disturbance caused by the vertical COM motion is compensated by utilizing the sensory feedback in the CPG. To obtain the desired output signals from the CPG, the CPG is optimized by the two-phase evolutionary programming (TPEP), which is suitable to solve the constrained optimization problems. By combining the MWPG with the CPG, stable bipedal walking with a larger stride is obtained. The validity of the proposed method is verified through real experiments for the small-sized bipedal robot, HanSaRam-IX.