Diffusion magnetic resonance imaging is a non-invasive technique used to characterize tissue microstructure by measuring the diffusion of water molecules. Conventional Q-space trajectory imaging (QTI) estimates diffusion using low-order moments; however, it often neglects higher-order moments, such as the skewness tensor, resulting in an incomplete representation of diffusion asymmetry and potential estimation bias. In this work, we propose QTI with skewness tensor constraints, a method that incorporates higher-order skewness tensors under positivity constraints to mitigate deviations in the estimation of lower-order moments caused by the omission of higher-order asymmetry information. Furthermore, we introduce linear trace-weighted and quadratic trace-weighted filters to enhance high-diffusion components while suppressing low-diffusion components. Extensive experiments conducted on public, noisy, and synthetic datasets demonstrate that our method yields estimates closer to the ground truth on synthetic data and exhibits superior robustness in noisy conditions.