An LED package having a dual structure for lateral emission of light includes an LED chip, a lower structure, a lower lens and an upper lens. The lower structure includes a pair of electric connection parts, a package body, and a transparent encapsulant filled in the recess of the package body to seal the LED chip. The upper-hemispheric lower lens is fixed to an upper part of the lower structure with a bottom part thereof attached to an upper surface of the transparent encapsulant. The funnel-shaped upper lens is fixed to an upper end of the lower lens, and includes an axially symmetrical reflecting surface for laterally reflecting light from the lower lens, and an emitting surface for laterally emitting light reflected from the reflecting surface. The upper lens and the lower lens are separately molded and combined together to easily manufacture and efficiently install the LED package.