The current automatic cognitive load measurement system based on MFCC and prosodic features does not take into account phase based speech information. This paper aims to improve the performance of the baseline system by introducing phase based features into the system. The additional features proposed are group delay features, all-pole model based FM features and zero crossing count based FM features. Decrease in performance is observed when phase based features are considered individually or when concatenated with baseline features. However, significant performance improvement is observed when group delay features are fused with baseline features using linear combination score level fusion.