To provide a method for producing a core-sheath conjugate monofilament of polyester for screen gauze, which has a high tenacity, high modulus, and slightly causes yarn shaving or scum in weaving a screen gauze.

In the method for producing a core-sheath conjugate monofilament for screen gauze, the core-sheath conjugate monofilament has the sheath component of a polyester obtained by copolymerizing a polyethylene terephthalate with a third component and the core component of a polyester having ethylene terephthalate as a main repeating unit. The core component polymer contains a phosphorus compound that is a phenylphosphonic acid metal salt or its derivative and/or a phenylphosphinic acid metal salt or its derivative and is continuously drawn without being wound once, after ejected from a spinneret.