  We investigate the masses of $cs \bar c \bar s$ tetraquark states in a
diquark-antidiquark picture employing the relativized quark model proposed by
Godfrey and Isgur. Only the antitriplet diquark states in color space are
calculated. The diquark masses are obtained with the relativized potential
firstly, and then the diquark and antidiquark are treated as the usual
antiquark and quark, respectively, and the masses of the tetraquark states are
obtained by solving the Schr\"{o}dinger equation with the relativized potential
between the diquark and antidiquark. The theoretical uncertainties induced by
screening effects are also taken into account. It is found that the resonance
of $X(4140)$ can be regarded as the $cs \bar c \bar s$ tetraquark ground
states, and the $X(4700)$ can be assigned as the $2S$ excited tetraquark state.
When the internal excited diquarks are taken into account, the resonance of
$X(4500)$ can be explained as the tetraquark composed of one $2S$ scalar
diquark and one scalar antidiquark. In our approach, the $X(4274)$ cannot be
explained as a tetraquark state, however, it can be a good candidate of the
conventional $\chi_{c1}(3^3P_1)$ state. In addition, other charmonium-like
states $\chi_{c0}(3915)$, $X(4350)$, $X(4630)$ and $X(4660)$, as the $cs \bar c
\bar s$ tetraquark states, are also discussed.
