Packed bed reactors have been widely applied in industrial production, such as for catalytic hydrogenation. Numerical simulations are essential for the design and scale-up of packed beds, especially direct numerical simulation (DNS) methods, such as the lattice-Boltzmann method (LBM), which are the focus of future researches. However, the large density difference between gas and liquid in packed beds often leads to numerical instability near phase interface when using LBM. In this paper, a lattice-Boltzmann (LB) model based on diffuse-interface phase-field is employed to simulate bubble rising in complex channels saturated with liquid, while the numerical problems caused by large liquid-to-gas density ratio are solved. Among them, the channel boundaries are constructed with regularly arranged circles and semicircles, and the bubbles pass through the channels accompanied by deformation, breakup, and coalescence behaviors. The phase-field LB model is found to exhibit good numerical stability and accuracy in handing the problem of the bubbles rising through the high-density liquid. The effects of channel structures, gas-liquid physical properties, and operating conditions on bubble deformation, motion velocity, and drag coefficient are simulated in detail. Moreover, different flow patterns are distinguished according to bubble behavior and are found to be associated with channel structure parameters, gravity Reynolds number (ReGr), and Eötvös number (Eo).