For meeting the actual demand of constant current (CC) and constant voltage (CV) in lithium-ion battery-charging process and improve the flexibility and safety of charging, this paper proposes a family of hybrid inductive power transfer (IPT) topologies that can realise CC and CV output and are not limited by the parameters of coils. Starting from a single existing topology with configurable CC or CV output, which can achieve zero-voltage switching (ZVS), load-independent and approximately zero reactive power, and the missing configurable CC or CV output is obtained by circuit transformation through cascaded T-type network. Then, the cascaded T-type network is switched by mode switches, so as to derive a family of hybrid IPT topologies suitable for lithium-ion battery wireless charging. In order to reduce the number of devices in the compensation network, the T-type network can be integrated with the existing compensation networks. Hence, this paper also proposes some hybrid IPT battery chargers and their design ideas. The control logic of mode switches and the sensitivity of compensation parameters are also discussed. Ultimately, a hybrid IPT battery charger based on S-S and S-LCC compensation networks is developed to test the correctness of the proposed scheme.