We report on the observation of spatially asymmetric turbulent structures with a long radial correlation length in the core of high-collisionality H-mode plasmas on DIII-D tokamak. These turbulent structures develop from shorter wavelength turbulence and have a radially elongated structure. The envelope of turbulence spans a broad radial range in the mid-radius region, leading to streamer-like transport events. The underlying turbulence is featured by intermittency, long-term memory effect, and the characteristic spectrum of self-organized criticality. The amplitude and the radial scale increase substantially when the shearing rate of the mean flow is reduced below the turbulent scattering rate. The enhanced LRRC transport events are accompanied by apparent degradation of normalized energy confinement time. These findings constitute the first experimental observation of long-radial-range turbulent transport events in high-collisionality H-mode plasmas, and demonstrate the role of mean shear flows in the formation and propagation of turbulence with long-radial-range correlation.