African swine fever (ASF) is transmitted by the African swine fever virus (ASFV). Since the early 1900s, ASF spread across Africa, Europe, South America and the Caribbean. In 2018, ASF was found in China and quickly spread to all provinces in mainland China, which had resulted in insecurity of pig production and serious economic losses. To investigate the effect of culling on the ASFV transmission in China, we formulate the nonlinear dynamic model of ASF with culling. The basic reproduction number is computed, and we investigate the nonlinear dynamic behaviors of the system. The uniform persistence of the system is proved. For the ASF model without culling, Lyapunov functions are used to show that the disease free equilibrium is globally asymptotically stable when the basic reproduction number is less than one, and the unique endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than one. Based on the mathematical model and data fitting, parameter values are estimated, sensitivity analysis is carried out and the effect of culling on ASFV transmission is investigated. The results show that the culling extremely diminishes the peak value of ASF cases and the cumulative number of ASF cases by over 99%. Our findings strongly suggest that culling may immensely contain the ASF spread. Meanwhile, improving the detection rate of symptomatic infectious pigs and taking sterilization measures on the farm may effectively suppress ASFV transmission. Our study may contribute to policy-makers preventing and controlling the spread of ASF.