CPU cache is limited but crucial storage on modern processor whereas the cache timing side-channel could indirectly leak data through the measurable timing variance. Speculative execution, a reason for the variance and a vital optimization in modern CPUs, can engender severe detriment to deliberate branch mispredictions. Though static analysis can qualitatively verify the timing-leakage-free property under speculative execution, it is incapable of producing endorsements including inputs and speculated flows to diagnose leaks in depth. This work proposes a new approach, Speculative symbolic Execution, for precisely validating cache timing leaks introduced by speculative execution. Generally, given a program with sensitive inputs (leakage-free in non-speculative execution), our method systematically explores the program state space. Meanwhile, it models speculative behavior at conditional branches and accumulates the cache side effects along with subsequent execution. Based on the dynamic exploration and a specified cache model, we construct leak conditions for memory accesses and conduct a constraint-solving based cache behavior analysis to generate leak witnesses. We have implemented our method in a tool named SpecuSym on KLEE, and evaluated it against 14 open-source benchmarks. Experiments show that SpecuSym successfully identified leaks in 6 programs on four different caches and eliminated false positives in 2 programs reported by recent work.