We describe a continuous-wave diode laser spectrometer for water-vapour precision spectroscopy at 1.38 μm. The spectrometer is based upon the use of a simple scheme for offset-frequency locking of a pair of extended-cavity diode lasers that allows to achieve unprecedented accuracy and reproducibility levels in measuring molecular absorption. When locked to the master laser with an offset frequency of 1.5 GHz, the slave laser exhibits residual frequency fluctuations of 1 kHz over a time interval of 25 minutes, for a 1-s integration time. The slave laser could be continuously tuned up to 3 GHz, the scan showing relative deviations from linearity below the 10{-6} level. Simultaneously, a capture range of the order of 1 GHz was obtained. Quantitative spectroscopy was also demonstrated by accurately determining relevant spectroscopic parameters for the 22,1→22,0line of the H2(18)O v1+v3 band at 1384.6008 nm.