In this paper, we propose and analyze a new interconnection network called triangle tower graph/network. It is maximally connected and tightly super-connected, for $n>4$ or $n=4$, i.e. the connectivity $\kappa(TT_{n})$ of $TT_{n}$ is $2n-3$. The star graph is a specific subgraph of the proposed triangle tower graph. Therefore, the triangle tower graph not only inherits many good capabilities possessed by the star graph (e.g., vertex symmetry, connectivity, vertex transition, etc.), but also shows that $S_{n}$ can be embedded into $TT_{n}$ with digit 1. The proposed triangle tower graph is superior to the traditional hypercube and bubble-sort graph with respect to diameter, connectivity and conditional vertex connectivity as that these three graphs have approximately similar numbers of vertices. The diameter and average distance are presented for the proposed network. We also propose one variety conjectures on Hamiltonicity of triangle tower graph and prove conjectures are true for $n=3,4$ and $n=5,6,~k=1,2$.