This work developed novel jute-yarn, non-crimp, unidirectional (UD) preforms and their composites, with three different types of warp jute yarns of varying linear densities and twists in the dry UD preforms, in order to present a possible solution to the detrimental effects of higher yarn twists and crimp at the warp–weft yarn interlacements of traditional, woven, preform-based composites on their mechanical properties. In the developed UD preforms, warp jute yarns were placed in parallel by using a wooden picture-frame pin board, with the minimal number of glass weft yarns to avoid crimp at the warp–weft yarns interlacements, which can significantly enhance the load-bearing ability of UD composites compared to traditional, woven, preform composites. It was found that an optimal combination of jute warp yarn linear densities and twists in the UD preforms is important to achieve the best possible mechanical properties of newly developed UD composites, because it encourages a proper polymer-matrix impregnation on jute fibres, leading to excellent fibre–matrix interface bonding. Composites made from the 25 lb/spindle jute warp yarn linear density (UD25) exhibited higher tensile and flexural properties than other UD composites (UD20, UD30). All the UD composites showed a much better performance compared to the traditional woven preform composites (W20), which were obviously related to the higher crimp and yarn interlacements, less load-carrying capacity, and poor fiber–matrix interfaces of W20 composites. UD25 composites exhibited a significant enhancement in tensile modulus by ~232% and strength by ~146%; flexural modulus by 138.5% and strength by 145% compared to W20 composites. This reveals that newly developed, non-crimp, UD preform composites can effectively replace the traditional woven composites in lightweight, load-bearing, complex-shaped composite applications, and hence, this warrants further investigations of the developed composites, especially on long-term and dynamic-loading mechanical characterizations.