  In this paper, we prove uniform subconvexity bounds for $GL(3)\times GL(2)$
$L$-functions in the $GL(2)$ spectral aspect and the $t$ aspect via a delta
method. More precisely, let $\phi$ be a Hecke--Maass cusp form for
$SL(3,\mathbb{Z})$ and $f$ a Hecke--Maass cusp form for $SL(2,\mathbb{Z})$ with
the spectral parameter $t_f$. Then for $t\in\mathbb{R}$ and any
$\varepsilon>0$, we have
  \[ L(1/2+it,\phi\times f) \ll_{\phi,\varepsilon}
(t_f+|t|)^{27/20+\varepsilon}. \] Moreover, we get subconvexity bounds for
$L(1/2+it,\phi\times f)$ whenever $|t|-t_f \gg (|t|+t_f)^{3/5+\varepsilon}$.
