Lithium rechargeable batteries are being currently highlighted as major energy storage systems due to their high energy and power density. However, it needs to find new electrode materials of lithium rechargeable batteries with excellent electrochemical properties, such as high capacity, good cyclability, and power capability for new applications to electric vehicles and large scale energy storage devices. To improve electrochemical properties of various electrode materials of lithium rechargeable batteries, graphene was selected because of its exceptionally excellent properties, such as high surface area, excellent electronic conductivity, and superior mechanical flexibility. In this study, various graphene-based hybrid materials were studied, such as $Co_3O_4$/graphene, $Mn_3O_4$/graphene, $SnO_2$/graphene, $FePO_4$/graphene, and $LiFePO_4$/graphene hybrid materials. These hybrid materials were fabricated from a simple and robust in-situ process. Chapter 2 describes the fabrication procedures and characterization results of the $Co_3O_4$/graphene, $Mn_3O_4$/graphene, and $SnO_2$/graphene hybrid materials. These hybrid materials were tested as anode materials for lithium rechargeable batteries. $Co_3O_4$, $Mn_3O_4$, and $SnO_2$ can exhibit high capacity, as the representative conversion and/or alloying reaction compounds, because these simple metal oxides can store more than single lithium ion through conversion and/or alloying reaction. However, conversion and/or alloying reactions cause a huge volume change during electrochemical reactions. Furthermore, insulating Li2O formed in the electrochemical reactions can result in low electronic conductivity; therefore, poor electrochemical performance. By incorporating graphene with high surface area, excellent elec-tronic conductivity, and superior mechanical flexibility, the problems resulting from large volume change during electrochemical reactions and poor electronic conductivity can be im-proved. In chapte...