In this paper we investigate the dynamics of an asymmetric exclusion process on a one-dimensional lattice with long-range hopping and random update via Monte Carlo simulations theoretically. Particles in the model will firstly try to hop over successive unoccupied sites with a probability q, which is different from previous exclusion process models. The probability q may represent the random access of particles. Numerical simulations for stationary particle currents, density profiles, and phase diagrams are obtained. There are three possible stationary phases: the low density (LD) phase, high density (HD) phase, and maximal current (MC) in the system, respectively. Interestingly, bulk density in the LD phase tends to zero, while the MC phase is goveed byα,β, and q. The HD phase is nearly the same as the normal TASEP, determined by exit rateβ. Theoretical analysis is in good agreement with simulation results. The proposed model may provide a better understanding of random interaction dynamics in complex systems.