In this paper, the oil-weathering model, which consists of four first order ordinary differential equations (ODEs), were solved by using two-point block backward differentiation formula (2BDF). The 2BDF method gives two approximations for each integration step with a fixed ratio of changing step sizes. These four ODEs provide solutions for the oil slick area, fraction of evaporation, fraction of emulsification, and fraction of dissolution for the oil spill. Subsequently, these solutions were used to calculate the changes in the oil spill density and viscosity. The result was generated for crude oil at the temperatures of 273K and 283K with the water content at a maximum of 80. Numerical solutions gained from 2BDF were plotted against the solutions from ode45. Error of computations between these two solvers suggests that the 2BDF can be an alternative method for the simulation of oil-weathering models. © 2022, Institute of Technology PETRONAS Sdn Bhd.