A method of hydroprocessing a heavy hydrocarbon feedstock using a hydroprocessing catalyst having specific properties making it effective in the hydroconversion of at least a portion of the heavy hydrocarbon feedstock to lighter hydrocarbons. The hydroprocessing catalyst comprises a Group VIB metal component (e.g., Cr, Mo, and W), a Group VIII metal component (e.g., Ni and Co) and, optionally, a potassium metal component that are supported on a support material comprising alumina. The alumina has novel physical properties that, in combination with the catalytic components, provide for the hydroprocessing catalyst. The hydroprocessing catalyst is particularly effective in the conversion of the heavy hydrocarbon feedstock. The alumina is characterized as having a high pore volume and a high surface area with a large proportion of the pore volume being present in the pores within a narrow pore diameter distribution about a narrowly defined range of median pore diameters. The support material preferably does not contain more than a small concentration of silica. The alumina component is preferably made by a specific method that provides for an alumina having the specific physical properties required for the hydroprocessing catalyst.