To obtain a new multi-purpose additive for a lubricating agent, especially improving the viscosity and dispersing characteristics of the lubricating agent, to provide a method for preparing such multi-purpose additive and to obtain a lubricating agent improving the dispersing and viscosity characteristics.

This dispersing agent-viscosity improving agent containing a metal for a lubricating oil is obtained by containing a reaction product of reactants containing the following (a) and (b), and (c) as necessary. (a) A hydrocarbon polymer grafted with an α,β-ethylenically unsaturated carboxylic acid or their functional derivative. (b) A derivative containing nitrogen and a metal of at least one kind of a derivative containing nitrogen and a metal of a polycarboxylic acid substituted by a hydrocarbon or their functional derivative and selected from the following (b-i) and (b-ii) groups; (b-i) an amide or an imide derivative of a metal salt; (b-ii) a metal complex of a non acidic acylated nitrogen compound. (c) At least one kind of a polyester containing hydroxyl group and at least one free hydroxyl group capable of performing condensation reaction.