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The recently improved observation of the fine structure constant has led to anegative $2.4\sigma$ anomaly of electron $g-2$. Combined with the long-existingpositive $4.2\sigma$ discrepancy of the muon anomalous magnetic moment, it isinteresting and difficult to explain these two anomalies with a consistentmodel without introducing flavor violations. We show that they can besimultaneously explained in the inverse seesaw extended next-to-minimalsupersymmetric standard model (ISS-NMSSM) by the Higgsino--sneutrinocontributions to $(g-2)_e$ and $(g-2)_\mu$. The spectrum features prefer light$\mu$, which can predict $m_Z$ naturally, and it is not difficult to obtain a$\tau$-type sneutrino dark matter candidate that is compatible with theobserved dark matter relic density and the bounds from dark matter directdetection experiments. Due to the compressed spectra and the undetectable decaymode of selectrons, they can evade the current Large Hadron Collider (LHC)constraints.

Electron and Muon Anomalous Magnetic Moments in the Inverse Seesaw Extended NMSSM