A weft insertion apparatus in a jet loom, wherein the weft insertion apparatus includes an auxiliary nozzle (21) for weft insertion having an injection hole (23) from which air jet is ejected to deliver a weft (Y) in a weft guiding passage (14), is provided. The injection hole (23) is tapered so that the cross-sectional area of the hole (23) is decreased toward the direction of air injection of the auxiliary nozzle (21). The ratio A of a tapered angle γ of the injection hole (23) to a processing deflection angle β of the injection hole (23), γ/β = A, has the relationship expressed by an inequality (1): A ≥ A ⁢ 0 wherein A0 is the value of γ/β when the variation range (Δδmax) of the jet deflection angle (δ) becomes 0 when the injection pressure of the auxiliary nozzle (21) is changed from the maximum pressure (Pmax) for weft insertion to the minimum pressure (Pmin) for weft insertion.