The initial cases of novel coronavirus (COVID-19) were identified in most West African countries between late February and early March of 2020. But it is only after March 15, 2020 that the number of cases started rising significantly in these countries. This study analyzes the transmission dynamics of the outbreak in West Africa nearly 5 months after the effective onset. We focus on Cameroon, Ghana, Guinea and Nigeria, which are the four West African countries with the highest numbers of infected cases. We combine models of mathematical epidemiology and publicly available data to estimate the main disease transmission characteristics. In particular, we estimate the initial doubling time, the peak time, the peak rate, the final size and the short-term transmission forecasts of the COVID-19 epidemic for these countries. Policy implications for the effectiveness of control measures and for assessing the potential impact on public health in West Africa are discussed.