Rotational acceleration of the head is known to be the cause of traumatic brain injuries. It was hypothesized that by introducing anisotropy in a foam liner in head protection applications, for example, protective helmets, rotational acceleration transmitted to the head can be further mitigated. Therefore, composite foam with a cylinder/matrix configuration with anisotropy at "macro level" is proposed as a smart structural solution to replace single layer foam headliners of the same weight and thickness. In this paper, a parametric study on the cylinder/matrix configuration is performed and the results are compared with these of single layer expanded polystyrene foam. The structure is subsequently optimized for the best performance in mitigation of rotational acceleration and velocity. Oblique impact results show that the parameters such as the number of cylinders in a given structure, and the compliance of the matrix foam significantly affect the extent of rotational acceleration and velocity mitigation. Optimized composite foam configurations are subsequently proposed and they demonstrate a mitigation of rotational acceleration and velocity up to 44 and 19%, respectively. Moreover, relevant global head injury criteria such as HIC (Head Injury Criterion), RIC (Rotational Injury Criterion), HIP max (Head Impact Power), GAMBIT (Generalised Acceleration Model for Brain Injury Threshold), and BrIC (Brain Injury Criterion) demonstrated reduction up to 27, 67, 31, 26, and 19%, respectively.