The notion of the maximal pattern complexity of words was introduced by Kamae and Zamboni. In this paper, we obtain an almost exact formula for the maximal pattern complexity $p^*_\alpha(k)$ of Toeplitz words $\alpha$ on an alphabet ${\mathbb A}$ defined by a sequence of coding words $(\eta^{(n)})^\infty\in({\mathbb A}\cup\{?\})^{\mathbb N}(n=1,2,\dotsc)$ including just one ‘?’ in their cycles $\eta^{(n)}$. Using this formula, we characterize pattern Sturmian words (i.e. $p^*_\alpha(k)=2k$ (for all $k$)) in this class. Moreover, we give a characterization of simple Toeplitz words in the sense of Kamae and Zamboni in terms of pattern complexity. In the case where $\eta^{(1)}=\eta^{(2)}=\dotsb$, we obtain the value $\lim_{k\to\infty}p_\alpha^*(k)/k$. We construct a Toeplitz word $\alpha\in{\mathbb A}^{\mathbb N}$ with $\#\A=2$ such that $p^*_\alpha(k)=2^k~(k=1,2,\dotsc)$, while Toeplitz words in our sense always have discrete spectra.