This paper mainly solves the problems of how to efficiently configure and calibrate a parabolic camera composed by one parabolic mirror and one traditional CCD camera, which satisfies the constraint of central projection. Firstly, the relationship between various configuration parameters and its corresponding system errors is tested and depicted using numerical simulation experiments, with which the range for best configuration parameters is obtained. Then, a new algorithm is suggested for calibrating the parabolic camera with the image information of a spatial plane. With the known intrinsic parameters, the calibration problem is formulated into a fourth order polynomial eigenvalue problem via the plane-induced Homographic matrix. An analytic solution is obtained to avoid the complicated numerical computation, and hence rapid calibration is achieved. The results also show that five or more pairs of corresponding image points are sufficient for solving this problem. Finally, numerical simulation and real data experiments are performed to validate the accuracy and robustness of the proposed algorithm, and satisfactory results are obtained in those experiments.