In this note, we study the regularity of Leray-Hopf weak solutions to the Navier-Stokes equation, with the condition $$ abla (u_{1},u_{2},0) in L^{frac{2}{1-r}}(0,T; dot{mathcal{M}}_{2,3/r} (mathbb{R}^3) , $$ where $dot{mathcal{M}}_{2,3/r}(mathbb{R}^3)$ is the Morrey-Campanato space for $0<r<1$. Since $$ L^{1/3}(mathbb{R}^3)subset dot{X}_r(mathbb{R}^3) subset dot{mathcal{M}}_{2,3/r}(mathbb{R}^3), $$ the above regularity condition allows us to improve the results obtained by Fan and Gao [6].