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Low-temperature and elastic properties of the quasicrystal approximant GdCd6 have been investigated by means of an ultrasonic measurement. Salient elastic anomalies were observed in the temperature and magnetic field dependence of the principal elastic constants, most probably being associated with the successive multiple magnetic phase transitions showing up at low temperatures. Based on the experimental data, a magnetic field vs temperature phase diagram was constructed. In a zero magnetic field, at least four phases appear to exist. However, the phase diagram both for the magnetic field applied for H// ⟨ 100 ⟩ and H// ⟨ 110 ⟩ is richer, and interestingly some phase boundaries correspond to the development of field-induced phases, leading to the intricate magnetic phase diagram possibly with multiple ordered phases. We discuss the elastic and electronic properties at low temperatures, and also the nature of the multiple magnetic phase transitions of GdCd6.