Li-ion hybrid capacitors, which combine the high energy densities of Li-ion batteries and high power densities of super capacitors, are a new type of energy storage device with large application potentials. In this study, a porous carbon nanomaterial (carbonized zeolitic imidazolate framework-8 (cZIF-8)) derived from metal organic frameworks (MOFs) was synthesised by pyrolysis of a MOF precursor at a high temperature. This carbon material had a large specific surface area, excellent porosity, good thermal stability, and high conductivity. A new type of Li-ion hybrid capacitor (cZIF-8//lithium titanate (LTO)) was constructed using a capacitor electrode based on cZIF-8 as a positive electrode and battery electrode based on LTO as a negative electrode. The assembled device had highest energy density of 44 W·h·kg^-1 and power density of 5387 W$\cdot$kg$^{-1}$, significantly higher than that of a cZIF-8//cZIF-8 supercapacitor (16.6 W·h·kg^-1). The Li-ion hybrid capacitor (cZIF-8//LTO) also exhibited a good cyclic performance (85.4% of the initial value after 10000 cycles) at a high current density of 2 A·g^-1. This MOF-based Li-ion hybrid capacitor enables to effectively increase the energy density of the electrochemical energy storage device without reducing the power capability.