Here we report on absolute frequency measurements of a commercial high power CW diode-pumped solid-state laser (Coherent Verdi-V5). This kind of lasers usually presents large frequency jitter (up to 50 MHz) both in the short term (1 ms time scale) and in the long term (>10 s time scale). A precise measurement of absolute frequency deviations in both temporal scales should require a set of different devices (optical cavities, optical wave-meters), each suited for measurements only at a specific integration time. Here we demonstrate how a frequency comb can be used to overcome this difficulty, allowing in a single step a full characterization of both short (<1 ms) and long term (> 103 s) absolute frequency jitter with a resolution better than 1 MHz. We demonstrate in this way the flexibility of optical frequency combs for absolute frequency measurements not only of ultra-stable lasers but also of relatively unstable lasers. The absolute frequency calibration of the Verdi laser that we have obtained have been used in order to improve the accuracy of the measurements of the local gravitational acceleration value with 88Sr atoms trapped in 1D vertical lattices.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.