The number of road accidents has increased annually over the last 20 years, and this is a matter of considerable concern. Automobile safety systems must therefore be carefully evaluated to ensure they are able to serve their purpose in protecting passengers. One of these safety systems is the car bumper system. The bumper system plays a vital role, especially in protection against frontal impact. In this study, using finite element analysis employing LS-DYNA software, we analyse the crash behaviour of bumper fascias made of unidirectional oil palm empty fruit bunch (OPEFB) fibre-reinforced polypropylene (PP) composites. The incorporation of OPEFB fibres into the bumper part stems from the growth of environmental concerns and is in line with national sustainable development goals. In this analysis, the composite bumper was subjected to a frontal low impact speed of 4 km h−1 in accordance with Part 581 of the Federal Motor Vehicle Safety Standard regulations enforced by the National Highway Traffic Safety Administration for low-velocity impacts. Comparative study was made with existing bumper materials, namely steel, aluminium alloy and PP. The effect of fibre orientation and fibre content of the composite on the crash performance of the bumper was also investigated. The fibre orientation was varied between vertical, 45° and horizontal directions while fibre content varied between 25%, 35%, 45% and 55%. Our results show that the composite bumper fascia has comparable specific energy absorption to existing bumper materials. An increase in the fibre content of the composite results in an increase in the energy absorption ability, while fibre orientation made no significant difference to the impact performance.