We consider a class of hypoelliptic operators of the following type $$L=sum_{i,j=1}^{p_0}a_{ij}{partial}^2_{x_ix_j}+sum_{i,j=1}^{N}b_{ij}x_i{partial}_{x_j}-{partial}_t$$, where ($a_{ij}$), ($b_{ij}$) are constant matrices and ($a_{ij}$) is symmetric positive definite on $mathbb{R}^{p_0}$ ($p_0{leqslant}N$). By establishing global Morrey estimates of singular integral on the homogenous space and the relation between Morrey space and weak Morrey space, we obtain the global weak Morrey estimates of the operator L on the whole space $mathbb{R}^{N+1}$.