Inclusion Criteria:  Male or female Elaprase naive participants (and who are not part of any other program at the time of study enrollment and during the study period) of any age with confirmed diagnosis of Hunter syndrome based on the following documented biochemical and genetic criteria:  Documented deficiency in iduronate 2-sulfatase (IDS [12S]) enzyme activity of less than or equal to 10 percent (%) of the lower limit of the normal range as measured in plasma, fibroblasts, or leukocytes (based on normal range of measuring laboratory). A normal enzyme activity level of one other sulfatase as measured in plasma, fibroblasts, or leukocytes (based on normal range of measuring laboratory). The participant has a documented mutation in the IDS gene. In the opinion of the investigator, the participant or the participant's parents/guardians are capable of understanding and complying with protocol requirements. The participant or, when applicable, the participant's parents/guardians/legal authorized representative (LAR) signs and dates a written, informed consent form and any required privacy authorization prior to the initiation of any study procedures. If the participant participating in this study is greater than or equal to (>=) 7 years and less than (<) 18 years of age signs and dates an assent form. A male participant who is nonsterilized and sexually active with a female partner of childbearing potential agrees to use barrier method of contraception (example, condom with or without spermicide) from signing of informed consent throughout the duration of the study. The female partner of a male participant should also be advised to use a highly effective/effective method of contraception. A female participant of childbearing potential who is sexually active with a nonsterilized male partner agrees to use a highly effective method of contraception from signing of informed consent throughout the duration of the study.  Exclusion criteria:  Participant has received hematopoietic stem cell transplant (HSCT) or a bone marrow transplant at any time. Participant is unable to comply with the protocol, example, uncooperative with protocol schedule, refusal to agree to all of the study procedures, inability to return for safety evaluations, or is otherwise unlikely to complete the study, as determined by the investigator. Participant is suffering from any comorbid conditions (including hepatic impairment, acute or chronic) or having any other clinical observation or history during the screening examination, which would interfere with the objectives of the study as per investigators judgement. The participant has a chronic kidney disease with estimated Glomerular Filtration rate less than 15 milliliter per minute per 1.73 meter square (mL/min/1.73 m^2) and/or is on dialysis. The participant is an immediate family member, study site employee, or is in a dependent relationship with a study site employee who is involved in conduct of this study (example, spouse, parent, child, sibling) or may consent under duress. The participant has a history of hypersensitivity or allergies to related compounds including any associated excipients. If female, the participant is pregnant or lactating or intending to become pregnant before participating in this study, during the study; or intending to donate ova during such time period. If male, the participant intends to donate sperm during the course of this study. The participant has participated in another clinical study or received any investigational compound or non-investigational idursulfase beta within the past 30 days before informed consent.