Pseudomonas aeruginosa is an opportunistic pathogen that causes a wide range of problematic infections in individuals with predisposing conditions. Infections can be treated with colistin but some isolates are resistant to this antibiotic. To better understand the genetic basis of resistance, we experimentally evolved 19 independent resistant mutants from the susceptible laboratory strain PAO1. Whole genome sequencing identified mutations in multiple genes including phoQ and pmrB that have previously been associated with resistance, pitA that encodes a phosphate transporter, and carB and eno that encode enzymes of metabolism. Individual mutations were engineered into the genome of strain PAO1. Mutations in pitA, pmrB and phoQ increased the minimum inhibitory concentration (MIC) for colistin 8-fold, making the bacteria resistant. Engineered pitA/phoQ and pitA/pmrB double mutants had higher MICs than single mutants, demonstrating additive effects on colistin susceptibility. Single carB and eno mutations did not increase the MIC suggesting that their effect is dependent on the presence of other mutations. Many of the resistant mutants had increased susceptibility to β-lactams and lower growth rates than the parental strain demonstrating that colistin resistance can impose a fitness cost. Two hundred and fourteen P. aeruginosa isolates from a range of sources were tested and 18 (7.8%) were colistin resistant. Sequence variants in genes identified by experimental evolution were present in the 18 resistant isolates and may contribute to resistance. Overall our results identify pitA mutations as novel contributors to colistin resistance and demonstrate that resistance can reduce fitness of the bacteria.