Road traffic accident in Nigeria is increasing at a worrying rate and has raised one of the country major concerns. We provided appropriate and suitable time series model for the consequences of road accident, the injured, killed and total casualty of the road accident in Nigeria. The most widely used conventional method, Autoregressive Integrated Moving Average (ARIMA) model of time series, also known as Box-Jenkins method is applied to yearly data on the consequences of road accident data in Nigeria from 1960-2013 to determine patterns of road traffic accident consequences; injured, killed and total casualty of the road accident along the Nigeria motorway. Appropriate models are developed for the accident consequences; injured, killed and total casualty. ARIMA (0; 2; 1) model is obtained for the injury and total casualty consequences, whilst ARIMA(1,2,2) model is obtained for the killed consequences, using the data from 1960-2011. The adequacy and the performance of the model are tested on the remaining data from 2012 to 2013. Seven years forecast are provided using the developed models and showed that road traffic accident consequences examined; injured, killed and total casualty would continue to increase on average.