We are witnessing the evolution that Machine Learning (ML) is applied to varied applications, such as intelligent security systems, medical diagnoses, etc. With this trend, it has high demand to run ML on end devices with limited resources. What's more, the fairness in these ML algorithms is mounting important, since these applications are not designed for specific users (e.g., people with fair skin in skin disease diagnosis) but need to be applied to all possible users (i.e., people with different skin tones). Brain-inspired hyperdimensional computing (HDC) has demonstrated its ability to run ML tasks on edge devices with a small memory footprint; yet, it is unknown whether HDC can satisfy the fairness requirements from applications (e.g., medical diagnosis for people with different skin tones). In this paper, for the first time, we reveal that the vanilla HDC has severe bias due to its sensitivity to color information. Toward a fair and efficient HDC, we propose a holistic framework, namely FE-HDC, which integrates the image processing and input compression techniques in HDC's encoder. Compared with the vanilla HDC, results show that the proposed FE-HDC can reduce the unfairness score by 90%, achieving fairer architectures with competitively high accuracy.