This paper solves the problem of how to energy-efficiently schedule sensor nodes and meet both constraints of the connected connectivity without accurate location information. Based on the theoretical analysis of the sensing coverage property of the minimal dominating set, the relationship between point coverage and area coverage in geometric graph is established. Based on the analytical results and Rule K algorithm which constructs the connected dominating set, a location-independent connected coverage protocol (LICCP) is proposed. Every sensor node adjusts the appropriate communication range. LICCP can provide the high quality of connected coverage using Rule K algorithm. Extensive simulation results show that the proposed connected coverage protocol can effectively maintain both high quality sensing coverage and connectivity in a long time.