Recent VLBA observation indicates the existence of an elongated (jet) structure in the compact radio source Sgr A^*. This is hard to explain in the context of advection-dominated accretion flow (ADAF) model for this source. On the other hand, the mass accretion rate favored by ADAF is 10-20 times smaller than that favored by the hydrodynamical simulation based on Bondi capture. If the latter were adopted, the predicted radio flux would significantly exceed the observation by about two orders of magnitude. A similar situation exists in the case of nearby giant ellipticals, where the canonical ADAF model - the widely assumed standard model for these sources - also significantly overpredict the radio flux. Based on these facts, in this paper we propose a truncated ADAF model for Sgr A^* and three ellipticals M87, NGC 4649 and NGC 4636. We assume that the accretion disk is truncated at a certain radius R_tr within which the jet forms by extracting the energy of the disk. The radio flux is greatly suppressed due to the radiative truncation of the disk and the fits to the observational data are excellent. For example, for Sgr A^*, the model fits the observational spectrum very well from radio including the ``excess'' below the break frequency to hard X-ray under a high accretion rate near the simulation value, and the predicted size-frequency relationship is also in excellent agreement with the observation; for M87, the predicted upper limit of the jet location is 24 R_g, in excellent agreement with the observational result that the jet is formed on scales smaller than 30 R_g, and the 20 % variability at 1 Kev - which is hard to explain in another model trying to explain the low radio flux of M87 - is also marginally interpreted. The success of the model supplies a possible piece of evidence for the disk rather than the hole origin for the powering of jets.