High-linearity electro-optic (EO) modulators play a crucial role in microwave photonics (MWP). Although various methods have been explored to enhance linearity in MWP links, they are often constrained by the intrinsic nonlinearity of modulator materials, the complexity of external control devices, the bulkiness of structures, and bandwidth limitations. In this study, we present an integrated thin-film lithium niobate (TFLN) linear Mach–Zehnder modulator (LMZM), showing, to our knowledge, a record-high spurious-free dynamic range (SFDR) of $121.7\mathrm{dB}·{\mathrm{Hz}}^{4/5}$ at 1 GHz with an optical power (OP) of 5.5 dBm into the photodetector (PD), based on a wide-bandwidth ($>50\mathrm{GHz}$) dual-optical-mode (TE0 and TE1) co-modulated configuration with just one RF input. Additionally, compared to conventional MZMs (CMZMs), the LMZM exhibits a $>10.6\text{-}\mathrm{dB}$ enhancement in SFDR with an OP of $>$$-8\mathrm{dBm}$ at 1 GHz, and maintains a 6.07-dB SFDR improvement even at 20 GHz with an OP of 0 dBm. The novel LMZM, featuring high linearity, wide bandwidth, structural simplicity, and high integration, holds significant potential as a key component in future large-scale and high-performance MWP integrated circuits.