Recently , a tight correlation among three quantities that characterize the prompt emission of long Gamma-Ray Bursts ( GRBs ) with known redshift z , was discovered \citep Firmani06 . We use this correlation to construct the Hubble diagram ( HD ) with a sample of 19 GRBs in the broad range of z = 0.17 - 4.5 , and carry out a full statistical analysis to constrain cosmological parameters ( CPs ) . To optimally solve the problem of circularity , a Bayesian approach is applied . The main result is that the concordance \Lambda CDM cosmology is fully consistent with the GRB data at the level of several tests . If we assume the \Lambda cosmology , then we find \Omega _ { m } = 0.31 ^ { +0.09 } _ { -0.08 } and \Omega _ { \Lambda } = 0.80 ^ { +0.20 } _ { -0.30 } ( 1 \sigma ) ; the flat-geometry case is within 1 \sigma . Assuming flatness , we find \Omega _ { m } = 0.29 ^ { +0.08 } _ { -0.06 } , and fixing \Omega _ { m } =0.28 , we obtain a dark energy equation of state parameter w = -1.07 ^ { +0.25 } _ { -0.38 } , i.e . the \Lambda CDM model ( w = -1 ) is within 1 \sigma . Given the low number of usable GRBs we can not yet constrain well the possible evolution of w = w ( z ) . However , the case w ( z ) = -1 ( \Lambda CDM ) is consistent at the 68.3 % CL with GRBs . It is shown also how a broad range of z ^ { \prime } s in the used sample improves the determination of CPs from the HD , which is the case of GRBs as distance indicators .