Cygnus X-1, as the first discovered black hole binary, is a key source for understanding the mechanisms of state transitions and the scenarios of accretion in extreme gravity fields. We present a spectral-timing analysis of observations taken with the Insight–Hard X-ray Modulation Telescope (HXMT) mission, focusing on the spectral-state-dependent timing properties in the broad energy range of 1−150 keV, thus extending previous studies based on Rossi X-ray Timing Explorer (RXTE) to both lower and higher energies. Our main results are the following: (a) We successfully use a simple empirical model to fit all spectra, confirming that the reflection component is stronger in the soft state than in the hard state. (b) The evolution of the total fractional root mean square (rms) depends on the selected energy band and the spectral shape, which is a direct result of the evolution of the power spectral densities (PSDs). (c) In the hard/intermediate state, we see clear short-term variability features and a positive correlation between the central frequencies of the variability components and the soft photon index Γ₁, which we also see at energies above 15 keV. In the soft state, the power spectrum is instead dominated by red noise. These behaviors can be traced to at least 90 keV. (d) Finally, the coherence and the phase-lag spectra show different behaviors, depending on the different spectral shapes.