We report the effects of electron doping on the crystal structure and electrical resistivity of LaOBiS$_{2-x}$F$_x$ (0.05 $leq$ $x$ $leq$ 0.2). The $ab$ plane is found to be relatively insensitive to the amount of F, whereas the $c$ axis shrinks continuously with increasing $x$, suggesting that the doped F atoms substitute selectively into the apical sites in the BiS$_2$ layer. At $x$ = 0.10, as the temperature is decreased from room temperature, the electrical resistivity is temperature-independent from room temperature to 285 K, increases linearly with decreasing temperature from 285 K to 205 K and then shows obvious insulating behavior below 205 K, which may be due to strong spin-orbit coupling. LaOBiS$_{1.9}$F$_{0.1}$ shows the significantly weak and temperature-independent diamagnetism without any evident anomalies caused by a phase transition.