Due to the complexity of biological systems, simulation of biological networks is necessary but sometimes complicated. The classic stochastic simulation algorithm (SSA) by Gillespie and its modified versions are widely used to simulate the stochastic dynamics of biochemical reaction systems. However, it has remained a challenge to implement accurate and efficient simulation algorithms for general reaction schemes in growing cells. Here, we present a modeling and simulation tool, called 'GeneCircuits', which is specifically developed to simulate gene-regulation in exponentially growing bacterial cells (such as E. coli) with overlapping cell cycles. Our tool integrates three specific features of these cells that are not generally included in SSA tools: 1) the time delay between the regulation and synthesis of proteins that is due to transcription and translation processes; 2) cell cycle-dependent periodic changes of gene dosage; and 3) variations in the propensities of chemical reactions that have time-dependent reaction rates as a consequence of volume expansion and cell division. We give three biologically relevant examples to illustrate the use of our simulation tool in quantitative studies of systems biology and synthetic biology.