  In this paper, we investigate the sums of mutliple zeta(-star) values of
height one: $Z_{\pm}(n)=\sum_{a+b=n} (\pm 1)^b\zeta(\{1\}^a,b+2)$,
$Z_{\pm}^{\star}(n)=\sum_{a+b=n} (\pm 1)^b\zeta^{\star}(\{1\}^a,b+2)$. In
particular, we prove that the weighted sum $\sum_{\substack{0\leq m\leq p\\ m:
{\rm even}}} \sum_{\mid\boldsymbol{\alpha}\mid=p+3} 2^{\alpha_{m+1}\
+1}\zeta(\alpha_0,\alpha_1,\ldots,\alpha_m,\alpha_{m+1}+1) $ can be evaluated
through the convolution of $Z_{-}(m)$ and $Z_{+}(n)$ with $m+n=p$.
