Sodium-ion batteries have attracted great attention since sodium is abundant and is low in cost. However, needs for development of new cathode materials are steadily increasing because conventional layered oxide $NaMO_2$ has limited energy density. Na-rich layered oxide $Na_2MO_3$ is attractive cathode material for alleviating the energy density issue. Here, we conduct first principles calculations for $Na_2MO_3$ (M = transition or post-transition metal) compounds. Through a systematic search based on properties including phase stability, operating voltage, and stability against oxygen loss, we provide several promising $Na_2MO_3$ compounds that are worthy of electrochemical evaluation.