Laser-based compact MeV X-ray sources are useful for a variety of applications such as radiography and active interrogation of nuclear materials. MeV X rays are typically generated by impinging the intense laser onto ~mm-thick high-Z foil. Here, we have characterized such a MeV X-ray source from 120 TW (80 J, 650 fs) laser interaction with a 1 mm-thick tantalum foil. Our measurements show X-ray temperature of 2.5 MeV, flux of 3 × 1012 photons/sr/shot, beam divergence of ~0.1 sr, conversion efficiency of ~1%, that is, ~1 J of MeV X rays out of 80 J incident laser, and source size of 80 m. Our measurement also shows that MeV X-ray yield and temperature is largely insensitive to nanosecond laser contrasts up to 10−5. Also, preliminary measurements of similar MeV X-ray source using a double-foil scheme, where the laser-driven hot electrons from a thin foil undergoing relativistic transparency impinging onto a second high-Z converter foil separated by 50–400 m, show MeV X-ray yield more than an order of magnitude lower compared with the single-foil results.