After the discovery of nematic topological superconductivity in CuxBi2Se3, carrier-doped topological insulators are established as a fertile ground for topological superconductors. The superconductor Cu1.5(PbSe)5(Bi2Se3)6 (CPSBS) contains Bi2Se3 blocks as a constitutional unit, but its superconducting gap appears to have nodes [S. Sasaki et al., Phys. Rev. B 90, 220504 (2014)], which is in contrast to the fully-opened gap in CuxBi2Se3 and the relation between the two superconductors remained an open question. Here we report our observation of clear two-fold symmetry in the in-plane magnetic-field-direction dependencies of the upper critical field and of the specific heat of CPSBS, where the direction of the maxima, which is different from that in CuxBi2Se3, indicates that the gap nodes are located in the mirror plane of the crystal lattice. This means that the topological nematic state with mirror-symmetry-protected nodes is realized in CPSBS.