A laser spectrometer based on a distributed-feedback semiconductor diode laser at 2 μm is developed to measure the changes of <sup>13</sup>CO<sub>2</sub>/<sup>12</sup>CO<sub>2</sub> isotope ratio in exhaled breath sample with the CO<sub>2</sub> concentration of ~4%. It is characterized by a simplified optical layout, in which a single detector and associated electronics are used to probe CO<sub>2</sub> spectrum. The cell has 10 cm long base length with 26.4 m optical path length in total and 330 cm<sup>3</sup> volume. The cell pressure and temperature are controlled at 50 Torr and 28℃, respectively. The best <sup>13</sup>δ precision of 0.06‰ was achieved by using wavelet denoising and Kalman filter.