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We numerically investigate a second harmonic generation (SHG) in a z-cut lithium niobate on insulator (LNOI) waveguide based on type-I mode phase matching (MPM) between two fundamental modes. A mode overlap factor that is close to unity is achieved and the normalized SHG efficiency reaches up to 72.1% W⁻¹cm⁻² at the telecommunication band, together with a large spectral tunability of 2.5 nm/K. Moreover, a bandwidth of about 100 nm for the broad SHG in a 5 mm-long LNOI ridge waveguide is demonstrated with this scheme. This stratagem will inspire new integrated nonlinear frequency conversion methods for versatile applications.