In this study, an image coding algorithm based on directional lifting wavelet transform (DLWT) and universal trellis-coded quantisation (UTCQ) is presented, and the coding performance is evaluated with three objective image quality metrics. Compared to the discrete wavelet transform, DLWT performing prediction and update along the direction of the local region can provide an efficient representation of edges in images, but shows a similar ability in representing the smooth region. To further improve the visual quality of the smooth background regions, UTCQ is adopted to quantising the wavelet coefficients. The proposed algorithm is measured with not only the dominant peak signal-to-noise ratio (PSNR), but also new metrics multi-scale structural similarity index measure (MSSIM) and visual information fidelity (VIF) which provide a better approximation to the perceived image quality than PSNR by taking the property of human visual system (HVS) into account. Experimental results show that the proposed algorithm has the best MSSIM and VIF performance among the compared algorithms (including JPEG2000) for the typical test images, and its decoded images at low bit-rate are visually more appealing in both edges and smooth background regions. For image Barbara, the proposed algorithm outperforms JPEG2000 up to 24.63% relatively in VIF and 1.93%dB in PSNR at 0.5%bpp, at most 3.62% relatively in MSSIM at 0.125%bpp. The experimental results also show that UTCQ does perform better than scalar quantisation (SQ) in MSSIM and VIF and improves the subjective visual quality, although UTCQ is not necessarily better than SQ in PSNR.