As one of the asymptotic formulas of the zeta-function, Hardy and Littlewood gave asymptotic formulas called the approximate functional equation. In this paper, we prove an approximate functional equation of the Barnes double zeta-function  Also, applying this approximate functional equation and the van der Corput method, we obtain upper bounds for  and  with respect to t as 

Barnes double zeta-function, approximate functional equation, Saddle point method, van der Corput method.