To produce polyester fiber and filament suitable for a sieve in a paper making machine, etc., wherein the sieve is prepared of a fiber using small amount of a terminal blocking agent, by producing a master batch using a high molecular carrier having no terminal groups reacting with the terminal blocking agent for polyester and the terminal blocking agent.

A master batch is produced using a high molecular carrier of ethylene, propylene, etc., having substantially no terminal groups reacting with a terminal blocking agent for polyester and the terminal blocking agent. The master batch is fed to a spinneret together with a fiber forming polyester material. Thus, even in the case where the content of the terminal blocking agent as a stabilizer is decreased to such a low level as to reduce environmental pollution or toxic effect on an operator, sufficient hydrolysis resistance can be imparted to a fiber or a filament.