Bitumen shows visco-elastic behavior in nature. It exhibits the property of elastic behavior and viscous behavior predicted by Dynamic response (E*) and phase angle (δ). Today’s modern world is facing the problem of early-stage fatigue cracks, rutting, and permanent deformations of asphalt bituminous pavements due to low temperature cracking, high-temperature deformation, moisture susceptibility, and overloading. The aforementioned pavement distresses result in the formation of potholes, alligator cracks, and certain types of deformations which result in early-stage cracking of bituminous pavements which accelerates the rehabilitation and maintenance cost. To properly address these issues, this study focused on the utilization of a waste source derived from surgical gloves named Nitrile Butadiene Rubber (NBR) as an additive to conventional asphalt pavement to study its effect in terms of stiffness. For this purpose, NBR was added in the intervals of 2%, 4%, 6%, and 8% to conventional bituminous pavement and rheological properties, marshall properties, dynamic modulus and phase angle was evaluated for varying NBR, temperature, and frequency. The dynamic response |E*| was determined using a simple performance tester (SPT) at four different temperatures 4.4°C, 21.1°C, 37.8°C, and 54.4°C and six different frequencies ranging from 0.1, 0.5, 1, 5, 10, and 25 Hz. Response surface methodology (RSM) was adopted to develop the relation between input and output and to optimize the amount of NBR in the mix based on dynamic modulus and phase angle. Based on the study it was concluded that the addition of NBR up to 6% increased the marshall stability while any further addition resulted in stability reduction. Similar behavior was observed in the case of dynamic modulus where the maximum dynamic modulus was observed as a result of 6% NBR addition irrespective of frequency and temperature. Based on the developed RSM model, it was concluded that coupling the NBR percentage with frequency increases the dynamic modulus for the same temperature and resulted highest dynamic modulus for 4.4°C while the dynamic modulus decreased as a result of increasing the temperature for the same combinations of NBR % and frequencies. From the numerical optimization, it was concluded that a maximum of 5.9% NBR could be added if it is intended to achieve the highest dynamic modulus and lowest phase angle.