This paper proposes two energy-efficient standby mode algorithms in short-range one-to-one 60GHz millimeter-wave (mmWave) communications. Among the many usage scenarios for mmWave radio, file downloading from kiosk terminals or peer-to-peer sync service with portable terminals are of great interest. For these portable terminals, reducing power consumption of standby mode as well as keeping connection setup time short is important. Comparing the power consumption between frame transmission and reception in short-range one-to-one 60GHz mmWave, the power consumed for a frame reception may become larger than that for a frame transmission. The proposed two energy-efficient standby mode algorithms for one-to-one communications assure the connection setup time and take each terminal's different requirement for reduction of its power consumption into consideration. In the proposed algorithms, each terminal accesses asynchronously and operates based on an interval consisting of several sub-intervals. In one proposed algorithm (Prop 1), a terminal transmits a connection request frame (CREQ) once every sub-interval and the other terminal waits for the CREQ during one sub-interval per interval. Thus, Prop 1 reduces the power consumption for CREQ transmission. In the other proposed algorithm (Prop 2), a terminal selects one sub-interval randomly for each interval and transmits CREQs repeatedly during that sub-interval. The other terminal waits for a CREQ during this CREQ transmission period at every sub-interval. Prop 2 saves the power consumption for a CREQ reception. We evaluate the power consumption of standby mode and connection setup time for Prop 1 and Prop 2 by both numerical analysis and computer simulations. We show that the power consumption of the CREQ waiting terminal with the proposed algorithms is more than 10mW lower than that with the conventional algorithm. We also show that our numerical analysis of the proposed algorithms derives the optimum parameters and facilitates system design. Next, we implement Prop 2 in a fully-integrated CMOS transceiver chip-set with antenna, RF/analog, PHY, and MAC for 60GHz proximity wireless communication. This experimental result is the same as the analysis result and it is verified that our proposed standby algorithm works as designed.