All of the AB_{2} Laves phases discovered so far satisfy the general crystalline structure characteristic of translational symmetry; however, we report here a new structured Laves phase directly precipitated in an aged Mg-In-Ca alloy by using aberration-corrected scanning transmission electron microscopy. The nanoprecipitate is determined to be a (Mg,In)_{2}Ca phase, which has a C14 Laves structure (hcp, space group: P6_{3}/mmc, a=6.25 Å, c=10.31 Å) but without any translational symmetry on the (0001)_{p} basal plane. The (Mg,In)_{2}Ca Laves phase contains two separate unit cells promoting the formation of five tiling patterns. The bonding of these patterns leads to the generation of the present Laves phase, followed by the Penrose geometrical rule. The orientation relationship between the Laves precipitate and Mg matrix is (0001)_{p}//(0001)_{α} and [11[over ¯]00]_{p}//[112[over ¯]0]_{α}. More specifically, in contrast to the traditional view that the third element would orderly replace other atoms in a manner of layer by layer on the close-packed (0001)_{L} plane, the In atoms here have orderly occupied certain position of Mg atomic columns along the [0001]_{L} zone axis. The finding would be interesting and important for understanding the formation mechanism of Laves phases, and even atom stacking behavior in condensed matter.