We study the effect of dimension variation for second-harmonic generation (SHG) in lithium niobate on insulator (LNOI) waveguides. Non-trivial SHG profiles in both type-0 and type-I quasi-phase matching are observed during the wavelength tuning of the fundamental light. Theoretical modeling shows that the SHG profile and efficiency can be greatly affected by the waveguide cross-section dimension variations, especially the thickness variations. In particular, our analysis shows that a thickness variation of tens of nanometers is in good agreement with the experimental results. Such investigations could be used to evaluate fabrication performance of LNOI-based nonlinear optical devices.