The fixed-time leader-following synchronization in a non-identical delayed network via non-chattering nonlinear control is investigated. By introducing a function of control error, a continuous and differential controller is constructed without using the sign function and absolution of the error. The sufficient conditions are then established to guarantee that synchronization errors converge exactly to zero within a fixed time interval. The proposed approach provides a high convergence for the network accurately tracking the trajectory of the leader. More importantly, a tighter bound for the settling time is obtained and the chattering effects are eliminated. The numerical simulations are conducted to illustrate the effectiveness of theoretical analysis.