A composite spinneret for discharging composite polymer streams composed of an island component polymer and a sea component polymer, which is composed of one or more distribution plates in which distribution holes and distribution grooves for distributing the polymer components are formed; and a lowermost layer distribution plate positioned to the downstream side of the distribution plate in the direction of the polymer spinning path, and having formed therein a plurality of island component discharge holes and a plurality of sea component discharge holes, wherein the sea component discharge holes are arranged on a virtual circular line C1 with a radius R1 centered on the island component discharge hole, the sea component discharge holes are arranged on a virtual circular line C2 with a radius R2 centered on the island component discharge hole, and the island component discharge holes are arranged on a virtual circular line C4 with a radius R4 centered on the island component discharge hole, and R1, R2 and R4 satisfy the following expression: R 2 ≥ R 4 ≥ √ 3 × R 1 and each discharge hole is arranged according to any one of the following conditions (a) to (d): condition (a) C1: three sea component discharge holes are arranged equally at a center angle of 120 degrees C2: three sea component discharge holes are arranged equally at a center angle of 120 degrees C4: six island component discharge holes are arranged equally at a center angle of 60 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 60 degrees θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 30 degrees condition (b) C1: three sea component discharge holes are arranged equally at a center angle of 120 degrees C2: three sea component discharge holes are arranged equally at a center angle of 120 degrees C4: three island component discharge holes are arranged equally at a center angle of 120 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 60 degrees θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 0 degree condition (c) C1: six sea component discharge holes are arranged equally at a center angle of 60 degrees C2: six sea component discharge holes are arranged equally at a center angle of 60 degrees C4: six island component discharge holes are arranged equally at a center angle of 60 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 0 degree θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 30 degrees condition (d) C1: four sea component discharge holes are arranged equally at a center angle of 90 degrees C2: eight sea component discharge holes are arranged C4: four island component discharge holes are arranged equally at a center angle of 90 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 26.6 degrees θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 0 degree. R 2 ≥ R 4 ≥ √ 3 × R 1 and each discharge hole is arranged according to any one of the following conditions (a) to (d): condition (a) C1: three sea component discharge holes are arranged equally at a center angle of 120 degrees C2: three sea component discharge holes are arranged equally at a center angle of 120 degrees C4: six island component discharge holes are arranged equally at a center angle of 60 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 60 degrees θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 30 degrees condition (b) C1: three sea component discharge holes are arranged equally at a center angle of 120 degrees C2: three sea component discharge holes are arranged equally at a center angle of 120 degrees C4: three island component discharge holes are arranged equally at a center angle of 120 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 60 degrees θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 0 degree condition (c) C1: six sea component discharge holes are arranged equally at a center angle of 60 degrees C2: six sea component discharge holes are arranged equally at a center angle of 60 degrees C4: six island component discharge holes are arranged equally at a center angle of 60 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 0 degree θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 30 degrees condition (d) C1: four sea component discharge holes are arranged equally at a center angle of 90 degrees C2: eight sea component discharge holes are arranged C4: four island component discharge holes are arranged equally at a center angle of 90 degrees θ3: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C2, is 26.6 degrees θ5: a phase angle between two discharge holes, one arranged on C1 and the other arranged on C4, is 0 degree.