Surface modification, such as hydrophobic network modification, is very promising technology to control droplet dynamics, heat transfer, and evaporation. However, fundamental mechanisms of how these chemically patterned surfaces affect the droplet evaporation dynamics and predictions of evaporation rates are still lacking. In the present work, we systematically investigated the full process of droplet evaporation dynamics on hydrophobic network surfaces and distinguished four different stages: constant contact line (CCL) stage, constant contact angle (CCA) stage, pattern-pinning (PP) stage, and moving contact line (MCL) stage. We further developed a general model considering the pinning and depinning forces to accurately predict the evaporation transition from PP to MCL stages (i.e., critical receding contact angle, θcr). As for the influence of the chemically patterned surface on the evaporation rate, a corrected contact line length was considered and combined with the well-known Rowan and Erbil's models. Finally, a general model was thus proposed and showed successful predictions for the evaporation durations of each stage.