Due to attractive material properties, thin film lithium niobate (TFLN) has emerged as a promising platform for advanced photonic functions such as high-speed electro-optical modulation, nonlinear frequency conversion, and frequency comb generation. The inevitable problems for the practical above-mentioned applications are the large coupling loss between the fiber and the TFLN waveguide and difficulty in achieving broadband coupling, especially covering the near-visible to near-infrared. Here, we theoretically propose a low-loss and ultrabroadband edge coupler with a six-layer structure. For transverse electric (TE) polarized light, the proposed coupler can achieve 0.62 dB, 0.38 dB, and 0.47 dB per facet at three common communication bands, 845 nm, 1310 nm, and 1550 nm, respectively. From 1200 nm to 2000 nm, the coupling loss is less than 1 dB/facet. Moreover, in the near-visible to near-infrared region ranging from 845 nm to 2000 nm, the coupling loss is lower than 2 dB/facet. The proposed coupler can avoid expensive electron beam lithography. Instead, it can be fabricated by i-line ultraviolet lithography, which is cost-effective and adaptable to wafer-scale fabrication. Also, simulated fabrication tolerances demonstrate the strong robustness of the proposed coupler. Our results pave a way towards practical TFLN photonic devices connected with optical fibers.