We present constraints on the values of \Omega _ { m } , n , \sigma _ { 8 } , obtained from measurements of the X-ray luminosity function of galaxy clusters as compiled in EMSS , RDCS and BCS galaxy cluster samples . The values obtained \Omega _ { m } = 0.25 ^ { +0.15 } _ { -0.05 } , n = -1 ^ { +0.05 } _ { -0.05 } , and \sigma _ { 8 } = 0.8 ^ { +0.1 } _ { -0.1 } are in agreement with WMAP data . We then put constraints on the quoted parameters and the dark-energy equation-of-state parameter , w , using Chandra observations of 37 clusters with < z > =0.55 derived from 400 deg ^ { 2 } ROSAT serendipitous survey and 49 brightest z \simeq 0.05 clusters detected in the All-Sky Survey . In the case of \Lambda CDM model , we get \Omega _ { m } = 0.25 ^ { +0.1 } _ { -0.08 } and \sigma _ { 8 } = 0.75 ^ { +0.08 } _ { -0.05 } , while in the case of the w CDM model , we get \Omega _ { m } = 0.28 ^ { +0.10 } _ { -0.10 } , w = -1.25 ^ { +0.30 } _ { -0.35 } , and \sigma _ { 8 } = 0.8 ^ { +0.09 } _ { -0.09 } . Our results are consistent with those from recent analyses of type Ia supernovae , cosmic microwave background anisotropies , the X-ray gas mass fraction of relaxed galaxy clusters , baryon acoustic oscillations and cosmic shear . The improvement in data quality from EMSS , RDCS , and BCS to Chandra observations leads to an improvement in the constraints even if not of the same entity of the improvement in data .