Most real-time planning algorithms address either the issue of response-time constraints or the issue of dynamic environments. A new real-time planning algorithm, DYNORA, is proposed to address both of these issues simultaneously. DYNORA is structured as a sequence of partial planning and execution cycles to avoid obsolescence of planning solutions at the time of execution. DYNORA uses a stopping criterion to balance planning cost and execution cost to achieve near optimal response times. DYNORA was used for the routing problem to optimize total cost. It shows better average-case time complexity than traditional real-time algorithms.