  Douglas metrics are metrics with vanishing Douglas curvature which is an
important projective invariant in Finsler geometry. To find more Douglas
metrics, in this paper we consider a class of Finsler metrics called general
$(\alpha,\beta)$-metrics, which are defined by a Riemannian metric
$\alpha=\sqrt{a_{ij}(x)y^iy^j}$ and a $1$-form $\beta=b_i(x)y^i$. We obtain the
differential equations that characterizes these metrics with vanishing Douglas
curvature. By solving the equivalent PDEs, the metrics in this class are
totally determined. Then many new Douglas metrics are constructed.
