Recently, nanoclay-based nanocomposites have gained much attentions in the preparation of drug delivery systems due to their excellent physicochemical properties. Herein, by the combination of magnetic laponite RD (laponite rapid dispersion; Lap) nanodiscs and chitosan (CS)/κ-carrageenan (Car) biopolymers, core–shell nanocarriers were fabricated to load and release of doxorubicin as anticancer drug model. The prepared nanocarriers not only showed great encapsulation efficiency (up to 95%) but also have excellent pH-responsiveness behavior to release of doxorubicin (DOX) drug in the acidic condition. During 240 h, the nanocarrier with high content of magnetic Lap (mLap) showed a cumulative release (CR) of DOX about 36.7% at pH 5.5, which was higher than in neutral condition (pH 7.4, 11.7%). In addition of pH-dependent release behavior, a sustained release of DOX was observed, which suggests the core–shell nanocarriers as a promising candidate in designing drug delivery systems with a prolonged drug release behavior.