Transmission line metamaterials based on composite right-left handed (CRLH) structures with pseudoperiodicity are proposed and analyzed experimentally. These metamaterials can be used in various microwave circuits to control not only amplitude but also phase responses of electromagnetic waves. Introducing some kinds of pseudoperiodicity can control phase responses of reflected waves, without affecting severely on electromagnetic bandgap (EBG) properties of periodic structures. Equivalent circuit approaches including distributed line sections are used to design non-periodic structures, resulting in an efficient design procedure. Pseudoperiodic design is also useful for homogenization of conventional metamaterials.