A recent addition to the many milling processes used in manufacturing to cut straight bevel gears (SBGs) is a new face-hobbing (FH) method that uses a virtual hypocycloid straight-lined mechanism to produce straight-lined teeth. Despite earning much attention because of its high productivity, however, this method is unable to handle lengthwise crowning on tooth surfaces, which results in poor contact performance. This paper therefore proposes a novel lengthwise crowning method, applicable on a modern six-axis computer numerical control (CNC) bevel gear cutting machine, in which the gear blank performs a swinging motion during machining. This swinging motion is enabled by machine setting modifications, which here are derived from a mathematical model of a double (profile and lengthwise) crowned gear. After the model's correctness is confirmed using ease-off and tooth contact analyses, a final investigation examines the effect of two key parameters related to contact performance indexes whose interrelations are graphed to provide a designer reference.