The distillation process plays an essential role in the petrochemical industry. However, the high-purity distillation column has complicated dynamic characteristics such as strong coupling and large time delay. To control the distillation column accurately, we proposed an extended generalized predictive control (EGPC) method inspired by the principles of extended state observer and proportional-integral-type generalized predictive control method; the proposed EGPC can adaptively compensate the system for the effects of coupling and model mismatch online and performs well in controlling time-delay systems. The strong coupling of the distillation column needs fast control, and the large time delay requires soft control. To balance the requirement for fast and soft control at the same time, a grey wolf optimizer with reverse learning and adaptive leaders number strategies (RAGWO) was proposed to tune the parameters of EGPC, and these strategies enable RAGWO to have a better initial population and improve its exploitation and exploration ability. The benchmark test results indicate that the RAGWO outperforms the existing optimizers for most of the selected benchmark functions. Extensive simulations show that the proposed method in terms of fluctuation and response time is superior to other methods for controlling the distillation process.