<p>This paper addresses complete synchronization and quasi-synchronization for Caputo-Hadamard fractional-order fuzzy neural networks (CFFNNs) with time delays and uncertain parameters (TDUPs). To begin with, two lemmas are introduced and strictly proved based on Caputo-Hadamard fractional theory, which plays a crucial role in studying synchronization problems of CFFNNs. Next, a new hybrid controller with Caputo-Hadamard fractional derivative and a nonlinear delayed feedback controller are respectively designed, and synchronization criteria of CFFNNs are gained according to lemmas we prove. Lastly, numerical simulations are presented to demonstrate effectiveness and feasibility of our results.</p>