In a Cu—Bi based sintered alloy, to which hard particles, such as Fe3P, are added, the main constituent components of the microstructure are a Cu matrix, Bi phase and the hard particles. In the sintering method of the present invention, the flow of the Bi phase is suppressed to as low level as possible. The novel structure is that the contact between the Bi phase and hard particles is kept to a low ratio. A lead-free bearing used for a fuel injection pump according to the present invention contains from 1 to 30 mass % of Bi and from 0.1 to 10 mass % of hard particles having from 10 to 50 μm of the average particle diameter, the balance being Cu and unavoidable impurities. The properties of the main component phases are utilized at a high level such that the sliding properties are equivalent to those of a Pb containing Cu-based sintered alloy.