Advanced driver assistance systems (ADAS) have matured over the past few decades with the dedication to enhance user experience and gain a wider market penetration. However, personalization components, as a means to make the current technologies more acceptable and trustworthy for users, has only recently been gaining momentum. In this work we develop an algorithm for learning personalized longitudinal driving behaviors via a Gaussian Process (GP) model. The proposed method learns from the individual driver's naturalistic car-following behaviors, and outputs a desired acceleration that suits the user's preference. The learned model can be used as a personalized adaptive cruise control (GP-PACC). The proposed GP-PACC is evaluated both with synthetic car-following data as well as driving simulation data obtained from the Unity game engine. Results show that the GP-PACC can accurately reproduce the acceleration and space gap trajectories even with reasonable measurement noises, and can capture the driving styles of a human driver up to 80% more accurately than baseline models such as an optimal velocity model and an intelligent driver model.