Organic phase change materials (PCMs) are commonly used for battery thermal management. Organic petroleum-based PCMs such as paraffin have an adverse effect on environment. Fatty acids as environmentally friendly bio-based PCMs, have enormous potential in sustainable development strategies. Nevertheless, the application of fatty acids in battery thermal management (BTMS) is restricted by the leakage of liquid PCM, poor thermal performance and the improper phase change temperature. We proposed a novel bio-based eutectic composite phase change materials (CPCM) with enhanced thermal conductivity and excellent shape-stabilization, composed of ethylene-vinyl acetate (EVA), Aluminum nitride (AlN), and the eutectic PCM of Lauric acid (LA) and Stearic acid (SA). Significantly, the screened eutectic PCM of LA-SA possesses a suitable phase change temperature(37.03 °C) corresponding to the battery operating temperature, and long-term thermal cycling stability of up to 100 cycles. And the cross-linked structure of EVA effectively encapsulated the eutectic PCM, whose mass only lost below 4% after being heated at 80 °C for 24 h. Simultaneously, the introduction of AlN can greatly improve their heat transfer ability and mechanical properties. LA-SA/EVA/AlN composites with 5 wt% AlN has adequate latent heat of 107.94 J.g−1 and high thermal conductivity of 0.726 W.(m·K)−1 as well as with low flexural strength of 1.72 MPa. Additionally, the proposed CPCM with 5 wt% AlN achieved the maximum temperature of battery below 45 °C during 4C discharging test. It suggested that the CPCM incorporated with AlN is capable effective cooling battery and dissipate energy inside PCM rapidly.