Projected climate change has stimulated increasing interest in the interactive effects between carbon dioxide (CO2) and temperature on crop yields. Crop yields are anticipated to decline if Earth continues to warm but increase as CO2 concentration rises. These two factors tend to work in opposite directions, and the interactive effect is not yet clear. There are also significant concerns that climate change is going to undermine global food security. Our purpose is to examine the quantitative relationship between CO2 and temperature on crop yields and to explore food security or insecurity in the presence of climate change. To do so, we perform a historical analysis on the crop yield trends in 57 selected countries from 1961 to 2013 on a yearly basis employing a fixed-effects panel regression model. The model is based on CO2 levels measured at Mauna Loa, Hawaii, and weighted-average temperatures in each country in corresponding years. We also incorporate other socio-economic factors, including purchasing power parity adjusted gross domestic product (PPP GDP) and education levels measured by Human Capital Index (HCI), that might affect crop yields. In addition, we control for other factors such as technological changes that contribute to increased yields. We find mixed evidence regarding CO2-fertilization and rising temperatures where some crops benefits and others are damaged. We identify four tipping points for CO2 beyond which CO2 is no longer beneficial for wheat, maize, rapeseed, and rice, where maize is expected to sustain benefits from CO2-fertilization up until 800 ppm. We also find that rice is damaged by rising temperatures beyond 44 °C.