Despite numerous studies about Marangoni instabilities, there are very few of them conducted for the menisci in microscale channels or tubes. In this paper, the onset of Marangoni flow on an initially isothermal meniscus in a capillary channel is studied. The temperature gradient perpendicular to the meniscus is found arousing a BACOnardaMarangoni instability when the channel size or the temperature gradient beyond certain values. The threshold Marangoni Number for the instability is obtained, which turns out to be dependent on the Biot Number. The evolution of the meniscus flow patterns with increasing Marangoni Number is studied. The influences of gravity are discussed. The present work is a preliminary step to a comprehensive understanding of Marangoni instability in capillary structures. The temperature gradient that is perpendicular to the meniscus should be paid attention to in the related applications.