We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of shear amplitudes, whose velocity fields are strikingly turbulent-like with vortices of different scales. The scaling behaviors of both the transverse velocity power spectra E T ( k ) ∝ k - α T and, more severely, the longitudinal velocity power spectra E L ( k ) ∝ k - α L are affected by the prominent peak centered around k ≈ 2π of the inter-particle distance due to the static structure factor of the hard-particle nature in contrast to the real turbulence. To reduce the strong peak effect to the actual values of α ν (the subscript ' ν ' refers to either T or L), we subsequently analyze the second-order velocity structure functions of S (2)ν( r ) in real space, which show the power-law scalings of S (2)ν( r ) ∝ r β ν for both modes. From the values of β ν , we deduce the corresponding α ν from the scaling relations of α ν = β ν + 2. The deduced values of α ν increase continuously with the shear amplitude γ m , showing no signature of yielding transition, and are slightly larger than α ν = 2.0 at the limit of γ m → 0, which corresponds to the elastic limit of the system, for all γ m . The inter-particle friction coefficients show no significant effect on the turbulent-like velocity fluctuations. Our findings suggest that the turbulent-like collective particle motions are governed by both the elasticity and plasticity in cyclically sheared granular materials.