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We have proposed a novel higher-order-mode dispersion compensating technique based on a hollow optical fiber mode converter. The mode converter shows the efficiency of more than 87% in conversion of the LP01 mode of single mode fibre (SMF) to the LP02 mode in a ring-core dispersion compensated fibre (DCF). Design parameters for the HOF and the mating ring-core DCF have been optimized, resulting in a very large average dispersion of -750 ps/nm/km in the C-band. Compensation of dispersion within 1 ps/nm/km, and dispersion slope within the range of -0.09 to 0.3 ps/nm2/km was estimated using 1.31 km of DCF for 60 km long SMF in the entire C-band.