Broadband frequency comb generation through cascaded quadratic nonlinearity remains experimentally untapped in free-space cavities with bulk χ(2) materials mainly due to the high threshold power and restricted ability of dispersion engineering. Thin-film lithium niobate (LN) is a good platform for nonlinear optics due to the tight mode confinement in a nano-dimensional waveguide, the ease of dispersion engineering, large quadratic nonlinearities, and flexible phase matching via periodic poling. Here we demonstrate broadband frequency comb generation through dispersion engineering in a thin-film LN microresonator. Bandwidths of 150 nm (80 nm) and 25 nm (12 nm) for center wavelengths at 1560 and 780 nm are achieved, respectively, in a cavity-enhanced second-harmonic generation (doubly resonant optical parametric oscillator). Our demonstration paves the way for pure quadratic soliton generation, which is a great complement to dissipative Kerr soliton frequency combs for extended interesting nonlinear applications.