Movement of intruder in jammed granular medium may result in interior reorganization of force chain structure. The form of drag force experienced by the intruder reflects the macro effect of the reorganization. By measuring the slow-pushing force of spheres intruding vertically into a granular bed, depth dependence of vertical drag force in jammed granular medium is studied experimentally. It is found that the drag force curve has a concave-convex transition with increasing penetration depth and the drag force follows different depth dependence in different regimes. In shallow regime, there is an exponent 1.3 power-law depth dependence; while in deep regime, the drag force is not saturated but has a tendency of power-law dependence with exponent 0.3. By studying the properties of the inflection point of the concave-convex transition, we have shown that the slowdown of the increasing rate of drag force is not a result of sidewall support proposed by previous researchers, but a result of volume effect of the intruder in granular medium. Moreover, the hydrostatic model is not appropriate in the case of slow drag and static granular bed, for not only the depth dependence of the drag force is higher than linear, but also its coefficient is much greater than the hydrostatic estimate.