As the most promising routing scheme in wireless sensor networks (WSNs), recently the research focus of geograph- ic routing is shifting towards duty-cycled sensor networks in which sensors are sleep scheduled to save energy consumption. However, nearly all research work about geographic routing in duty-cycled sensor networks ignore the fact that sensors can be mobile and almost all these work try to make geographic routing work in duty-cycled sensor networks from the view of changing the geographic forwarding mechanism, except the connected-k neighborhood (CKN) sleep scheduling algorithm and the geographic routing oriented sleep scheduling (GSS) algorithm. In this paper, focusing on geographic routing in duty- cycled mobile sensor networks, from the perspective of sleep scheduling, we propose two geographic-distance based connected- k neighborhood (GCKN) sleep scheduling algorithms. The first one is the geographic-distance based connected-k neighborhood for first path (GCKNF) sleep scheduling algorithm. The second one is the geographic-distance based connected-k neighborhood for all paths (GCKNA) sleep scheduling algorithm. By theoretical analysis and further evaluation, we show that when there are mobile sensors, geographic routing can achieve much shorter average length for 1) the first transmission path explored in a GCKNF sleep scheduling based sensor network and 2) all transmission paths searched in a GCKNA sleep scheduling based sensor network, compared with that in a CKN sleep scheduling based sensor network and in a GSS based sensor network.