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In the real traffic, drivers often perceive traffic information with delay time, while presenting asynchronous reactions that form non-constant delay time. Meanwhile, on-ramps are very common in the real traffic network environment, especially on highway sections. Traffic flow merging from the on-ramps has a significant impact on the traffic stability of the main road. Given these facts, we develop an extended lattice hydrodynamic model with drivers' continuous delay time and on-ramp. Based on the linear and nonlinear stability analysis, we derive the stability criterion and modified Korteweg–de Vries (mKdV) equation of the proposed lattice model; the kink-antikink soliton wave solution obtained by solving the above mKdV equation can be used to describe the propagation and evolution characteristics of density waves near the neutral stable curve. Results show that the ramp inflow ratio and delay time have a significant impact on the stability of traffic flow on the freeway main lane. [ABSTRACT FROM AUTHOR]