The evolution of drug resistance among pathogenic bacteria has led public health workers to rely increasingly on multidrug therapy to treat infections. Here, we compare the efficacy of combination therapy (i.e., using two antibiotics simultaneously) and sequential therapy (i.e., switching two antibiotics) in minimizing the evolution of multidrug resistance. Using in vitro experiments, we show that the sequential use of two antibiotics against Pseudomonas aeruginosa can slow down the evolution of multiple-drug resistance when the two antibiotics are used in a specific order. A simple population dynamics model reveals that using an antibiotic associated with high costs of resistance first minimizes the chance of multidrug resistance evolution during sequential therapy under limited mutation supply rate. As well as presenting a novel approach to multidrug therapy, this work shows that costs of resistance not only influences the persistence of antibiotic-resistant bacteria but also plays an important role in the emergence of resistance.