We present the first unbiased source catalogue of the Monitor of All-sky X-ray Image (MAXI) mission at high Galactic latitudes (|b| > 10°), produced from the first 7-month data (2009 September 1 to 2010 March 31) of the Gas Slit Camera in the 4--10 keV band. We develop an analysis procedure to detect faint sources from the MAXI data, utilising a maximum likelihood image fitting method, where the image response, background, and detailed observational conditions are taken into account. The catalogue consists of 143 X-ray sources above 7 sigma significance level with a limiting sensitivity of ~1.5 x 10^{-11} ergs cm^{-2} s^{-1} (1.2 mCrab) in the 4--10 keV band. Among them, we identify 38 Galactic/LMC/SMC objects, 48 galaxy clusters, 39 Seyfert galaxies, 12 blazars, and 1 galaxy. Other 4 sources are confused with multiple objects, and one remains unidentified. The log N - log S relation of extragalactic objects is in a good agreement with the HEAO-1 A-2 result, although the list of the brightest AGNs in the entire sky has significantly changed since that in 30 years ago.