For a prime number p, let $mathbb{Q}_p$ denote the p-adic field and let $mathbb{Q}_p^d$ denote a vector space over $mathbb{Q}_p$ which consists of all d-tuples of $mathbb{Q}_p$. For a function f ${in}L_{loc}^1(mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $mathbb{Q}_p^d$ by $$M_pf(x)=supfrac{1}{gamma{in}mathbb{Z}|B_{gamma}(x)|H}{int}_{Bgamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $mathbb{Q}_p^d$ and $B_gamma(x)$ denotes the p-adic ball with center x ${in};mathbb{Q}_p^d$ and radius $p^gamma$. If 1 < q $leq;infty$, then we prove that $M_p$ is a bounded operator of $L^q(mathbb{Q}_p^d)$ into $L^q(mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(mathbb{Q}_p^d)$, that is to say, |{$x{in}mathbb{Q}_p^d:|M_pf(x)|$>$lambda$}|$_H{leq}frac{p^d}{lambda}||f||_{L^1(mathbb{Q}_p^d)},;lambda$ > 0 for any f ${in}L^1(mathbb{Q}_p^d)$.