  We study the stochastic six-vertex model on a strip
$$\left\{(x,y)\in\mathbb{Z}^2: 0\leq y\leq x\leq y+N\right\}$$ with two open
boundaries. We develop a `matrix product ansatz' method to solve for its
stationary measure, based on the compatibility of three types of local moves of
any down-right path. The stationary measure on a horizontal path turns out to
be a tilting of the stationary measure of the asymmetric simple exclusion
process (ASEP) with two open boundaries. Similar to open ASEP, the statistics
of this tilted stationary measure as the number of sites $N\rightarrow\infty$
(with the bulk and boundary parameters fixed) also exhibit a phase diagram,
which is a tilting of the phase diagram of open ASEP. We study the limit of
mean particle density as an example.
