We present the results of a CO line survey of 30 galaxies at moderate redshift ( z \sim 0.2-0.6 ) , with the IRAM 30m telescope , with the goal to follow galaxy evolution and in particular the star formation efficiency ( SFE ) as defined by the ratio between far-infrared luminosity and molecular gas mass ( L _ { FIR } /M ( H _ { 2 } ) ) . The sources are selected to be ultra-luminous infrared galaxies ( ULIRGs ) , with L _ { FIR } larger than 2.8 10 ^ { 12 } L _ { \odot } , experiencing starbursts ; adopting a low ULIRG CO-to-H _ { 2 } conversion factor , their gas consumption time-scale is lower than 10 ^ { 8 } yr. To date only very few CO observations exist in this redshift range that spans nearly 25 % of the universe ’ s age . Considerable evolution of the star formation rate is already observed during this period . 18 galaxies out of our sample of 30 are detected ( of which 16 are new detections ) , corresponding to a detection rate of 60 % . The average CO luminosity for the 18 galaxies detected is L ’ _ { CO } = 2 10 ^ { 10 } K km s ^ { -1 } pc ^ { 2 } , corresponding to an average H _ { 2 } mass of 1.6 10 ^ { 10 } M _ { \odot } . The FIR luminosity correlates well with the CO luminosity , in agreement with the correlation found for low and high redshift ULIRGs . Although the conversion factor between CO luminosity and H _ { 2 } mass is uncertain , we find that the maximum amount of gas available for a single galaxy is quickly increasing as a function of redshift . Using the same conversion factor , the SFEs for z \sim 0.2-0.6 ULIRGs are found to be significantly higher , by a factor 3 , than for local ULIRGs , and are comparable to high redshift ones . We compare this evolution to the expected cosmic H _ { 2 } abundance and the cosmic star formation history .