Although significant advances in the design of soft robotic hands have been made to mimic the structure of the human hands, there are great challenges to control them for coordinated and human-like postures. Based on the principle of postural synergies in the human hand, we present a synergistic approach for coordinated control of a soft robotic hand to replicate the human-like grasp postures. To this end, we firstly develop a kinematic model to describe the control variables and the various postures of the soft robotic hand. Based on the postural synergies, we use the developed model and Principal Component Analysis (PCA) method to describe the various postures of the soft robotic hand in a low-dimensional space formed by the synergies of actuator motions. Therefore, the coordinates of these synergies can be used as low-dimensional control inputs for the soft robotic hand with a higher-dimensional postural space. Finally, we establish an experimental platform on a customized soft robotic hand with 6 pneumatical actuators to verify the effectiveness of the development. Experimental results demonstrate that with only a 2-dimensional control input, the soft robotic hand can reliably replicate 30 grasp postures in the Feix taxonomy of the human hand.