Integrated thin-film lithium niobate platform has recently emerged as a promising candidate for next-generation, high-efficiency wavelength conversion systems that allow dense packaging and mass-production. Here we demonstrate efficient, phase-matched second harmonic generation in lithographically-defined thin-film lithium niobate waveguides with sub-micron dimensions. Both modal phase matching in fixed-width waveguides and quasi-phase matching in periodically grooved waveguides are theoretically proposed and experimentally demonstrated. Our low-loss (~3.0 dB/cm) nanowaveguides possess normalized conversion efficiencies as high as 41% W-1cm-2.