A similar concern was demonstrated by Thomas Malthus 200 years ago. Population grows exponentially, Malthus explained, while food production grows at the slower arithmetic rate. Everything else the same, starvation would be indisputable.
Everything else is not the same. Crop yield is not constant, it has increased (see chart). The United States provides a good example of how population and food production have grown in a region with a strong rule of law. While corn yield has doubled nearly every ten years over the past half century, it took the population 36 years to double. At current rates of growth, it will be the next century before population doubles again. The growth in yield for other crops, such as wheat and rice, has also exceeded population growth rates (data here). In the end we are growing more food on less land, feeding ourselves and helping to feed the world.
Adapted from Environmental Trends.