Spatiotemporal vortices (STOVs) are a new, to the best of our knowledge, type of structured light in which the optical phase circulates in space-time. In this work, we propose to generate STOVs via second harmonic generation in lithium niobate nonlinear photonic crystals (NPCs) with a linearly chirped Gaussian pulse as the fundamental wave. The structural function of the NPC is derived by the inverse design method. Numerical simulations of the intensity and phase profiles of the generated second harmonic waves are performed with both the amplitude-phase-modulated and the simplified binary-phase-modulated NPCs. We anticipate our study will be valuable for the experimental generation and manipulation of STOVs in NPCs.