We propose a new type of multi-objective genetic programming (MOGP) for multi-objective design exploration (MODE). The characteristic of the new MOGP is the simultaneous symbolic regression to multiple objective functions using correlation coefficients. This methodology is applied to non-dominated solutions of the multi-objective design optimization problem to extract information between objective functions and design parameters. The result of MOGP is symbolic equations that are highly correlated to each objective function through a single GP run. These equations are also highly correlated to several objective functions. The results indicate that the proposed MOGP is capable of finding new design parameters more closely related to the objective functions than the original design parameters. The proposed MOGP is applied to the test problem and the practical design problem to evaluate the capability.