Introduction: Chronic Obstructive Pulmonary Disease (COPD) is a progressive disease that causes long-term breathing problems. The reliable monitoring of respiratory rate (RR) is very important for the treatment and management of COPD. Based on inkjet printing technology, we have developed a stretchable and wearable sensor that can accurately measure RR on normal subjects. Currently, there is a lack of comprehensive evaluation of stretchable sensors in the monitoring of RR on COPD patients. We aimed to investigate the measurement accuracy of our sensor on COPD patients. Methodology: Thirty-five patients (Mean ± SD of age: 55.25 ± 13.76 years) in different stages of COPD were recruited. The measurement accuracy of our inkjet-printed (IJPT) sensor was evaluated at different body postures (i.e., standing, sitting at 90°, and lying at 45°) on COPD patients. The RR recorded by the IJPT sensor was compared with that recorded by the reference e-Health sensor using paired T-test and Wilcoxon signed-rank test. Analysis of variation (ANOVA) was performed to investigate if there was any significant effect of individual difference or posture on the measurement error. Statistical significance was defined as p-value less than 0.05. Results: There was no significant difference between the RR measurements collected by the IJPT sensor and the e-Health reference sensor overall and in three postures (p > 0.05 in paired T-tests and Wilcoxon signed-rank tests). The sitting posture had the least measurement error of −0.0542 ± 1.451 bpm. There was no significant effect of posture or individual difference on the measurement error or relative measurement error (p > 0.05 in ANOVA). Conclusion: The IJPT sensor can accurately measure the RR of COPD patients at different body postures, which provides the possibility for reliable monitoring of RR on COPD patients.