Big longitudinal data provide more reliable information for decision making and are common in all kinds of fields. Trajectory pattern recognition is in an urgent need to discover important structures for such data. Developing better and more computationally-efficient visualization tool is crucial to guide this technique. This paper proposes an enhanced projection pursuit (EPP) method to better project and visualize the structures (e.g. clusters) of big high-dimensional (HD) longitudinal data on a lower-dimensional plane. Unlike classic PP methods potentially useful for longitudinal data, EPP is built upon nonlinear mapping algorithms to compute its stress (error) function by balancing the paired weights for between and within structure stress while preserving original structure membership in the high-dimensional space. Specifically, EPP solves an NP hard optimization problem by integrating gradual optimization and non-linear mapping algorithms, and automates the searching of an optimal number of iterations to display a stable structure for varying sample sizes and dimensions. Using publicized UCI and real longitudinal clinical trial datasets as well as simulation, EPP demonstrates its better performance in visualizing big HD longitudinal data.