Developing natural “free space” frequency upconversion is essential for photonic integrated circuits. In a single-crystal lithium niobate thin film planar waveguide of less than 1 μm thickness, we achieve type I and type II mode phase-matching conditions simultaneously for this thin film planar waveguide. Finally, by employing the mode phase matching of $\mathrm{e}+\mathrm{e}\to \mathrm{e}$ with $d_{33}$ at 1018 nm, we successfully achieve a green second-harmonic wave output with the conversion efficiency of $0.12\%/(\mathrm{W}·{\mathrm{cm}}^2)$, which verifies one of our simulation results. The rich mode phase matching for three-wave mixing in a thin film planar waveguide may provide a potential application in on-chip frequency upconversions for integrated photonic and quantum devices.