To optimise the pump source for a high-power diodepumped rubidium vapour laser, we have designed a laser diode array (LDA) with a narrowed and tunable linewidth and an external cavity formed by two volume Bragg gratings (VBGs). Through controlling the temperature differences between the two VBGs, the LDA linewidth, which was 1.8 nm before mounting the two VBGs, was tunable from 100 pm to 0.2 nm, while the output power changed by no more than 4 %. By changing simultaneously the temperature in both VBGs, the centre wavelength in air of the linewidth-tunable LDA was tunable from 779.40 nm to 780.05 nm.