The objective of this study is to prepare lead-free thick film resistor (TFR) paste compatible with AlN substrate for hybrid microelectronics. For this purpose, CaO-ZnO-$B_2O_3-Al_2O_3-SiO_2$ glass system was chosen as a sintering aid of $RuO_2$. The effects of the weight ratio of CaO to ZnO in glass composition, the glass content and the sintering temperature on the electrical properties of TFR were investigated. $RuO_2$ as a conductive and glass powder were dispersed in an organic binder to obtain printable paste and then thick-film was formed by screen printing, followed by sintering at the range between $750^{circ}C$ and $900^{circ}C$ for 10 min with a heating rate of $50^{circ}C$/min in an ambient atmosphere. The addition of ZnO to glass composition and sintering at higher temperature resulted in increasing sheet resistance and decreasing temperature coefficient of resistance. Using $RuO_2$-based resistor paste containing 40 wt%glass of CaO-20.5%ZnO-25%$B_2O_3$-7%$Al_2O_3$-15%$SiO_2$ composition, it is possible to produce thick film resistor on AlN substrate with sheet resistance of $10.6Omega/spuare$ and the temperature coefficient of resistance of 702ppm/$^{circ}C$ after sintering at $850^{circ}C$.