Urban sprawl and income segregation are two undesired urban patterns that occur during urban development. Empirical studies show that income level and inequality are positively correlated with urban sprawl and income segregation, respectively. However, the relationship between urban sprawl and income segregation is not only rarely investigated but also shows ambiguous empirical results when it is. Therefore, in this study, we built a stylized agent-based model with individual behaviours based on Alonso’s bid rent theory and ran simulations with different combinations of income level and income inequality. We measured the overall emergent patterns with indicators for urban sprawl and income segregation. The model confirms the established positive correlations between income level and urban sprawl and between income inequality and segregation. Furthermore, the model shows a negative correlation between urban sprawl and income segregation under free market conditions. The model indicates that without any policy implementation, a city will either suffer from urban sprawl or income segregation. Thus, this study serves as a starting point to study the effects of different urban planning policies on these two urban problems.