An apparatus for simulating an open candle flame having a swing holder located within a casing and engaging with a connecting rod, the connecting rod pivotally and rotatably connecting to the swing holder to form a first pivot structure for allowing the connecting rod to turn about a first axis, the swing holder pivotally and rotatably connecting to the casing to form a second pivot structure for allowing the swing holder and the connecting rod to turn about a second axis. The swinging mechanism of the apparatus is able to minimize the cost and the number of parts, ease and simplify assembly, and insure the flame display stays in place after manufacturing and during transit and handling.