Background Since March 11, 2020 when the World Health Organization (WHO) declared the COVID-19 pandemic, the number of infected cases, the number of deaths, and the number of affected countries have climbed rapidly. To understand the impact of COVID-19 on public health, many studies have been conducted for various countries. To complement the available work, in this article we examine Canadian COVID-19 data for the period of March 18, 2020 to August 16, 2020 with the aim to forecast the dynamic trend in a short term. Method We focus our attention on Canadian data and analyze the four provinces, Ontario, Alberta, British Columbia, and Quebec, which have the most severe situations in Canada. To build predictive models and conduct prediction, we employ three models, smooth transition autoregressive (STAR) models, neural network (NN) models, and susceptible-infected-removed (SIR) models, to fit time series data of confirmed cases in the four provinces separately. In comparison, we also analyze the data of daily infections in two states of USA, Texas and New York state, for the period of March 18, 2020 to August 16, 2020. We emphasize that different models make different assumptions which are basically difficult to validate. Yet invoking different models allows us to examine the data from different angles, thus, helping reveal the underlying trajectory of the development of COVID-19 in Canada. Finding The examinations of the data dated from March 18, 2020 to August 11, 2020 show that the STAR, NN, and SIR models may output different results, though the differences are small in some cases. Prediction over a short term period incurs smaller prediction variability than over a long term period, as expected. The NN method tends to outperform other two methods. All the methods forecast an upward trend in all the four Canadian provinces for the period of August 12, 2020 to August 23, 2020, though the degree varies from method to method. This research offers model-based insights into the pandemic evolvement in Canada.