Initiated from Nakamoto's Bitcoin system, blockchain technology has demonstrated great capability of building secure consensus among decentralized parties at Internet-scale, i.e., without relying on any centralized trusted party. Nowadays, blockchain systems find applications in various fields. But the performance is increasingly becoming a bottleneck, especially when permissionless participation is retained for full decentralization. In this work, we present a new consensus protocol named GHAST (Greedy Heaviest Adaptive Sub-Tree) which organizes blocks in a Tree-Graph structure (i.e., a directed acyclic graph (DAG) with a tree embedded) that allows fast and concurrent block generation. GHAST protocol simultaneously achieves a logarithmically bounded liveness guarantee and low confirmation latency. More specifically, for maximum latency $d$ and adversarial computing power bounded away from 50\%, GHAST guarantees confirmation with confidence $\ge 1-\varepsilon$ after a time period of $O(d\cdot \log(1/\varepsilon))$. When there is no observable attack, GHAST only needs $3d$ time to achieve confirmation at the same confidence level as six-block-confirmation in Bitcoin, while it takes roughly $360d$ in Bitcoin.