The near-field turbulent structure of double-concentric hydrogen-air jet diffusion flames, with or without swirl, has been investigated using conditionally sampled, three-component laser-Doppler velocimetry and coherent anti-Stokes Raman spectroscopy. The turbulent flame zone became thinner and shifted inward as the mean jet velocity was increased, whereas swirl created a radial velocity even at the jet-exit plane, thereby broadening and shifting the flame zone outward. The probability-density functions of velocity components, their 21 moments (up to fourth order), mean temperature, and root-mean-square temperature fluctuation were determined in the near field. The data can be used to validate advanced turbulent combustion models.