TransCon CNP administered once-weekly in children and adolescents with achondroplasia who have completed a prior TransCon CNP clinical trial. Participants who complete a prior TransCon CNP trial and meet all eligibility criteria will be invited to continue into the long-term open label extension trial to receive 100 µg CNP/kg/week of TransCon CNP. Trial treatment will be completed when the participant reaches 16 years of age for females and 18 years of age for males and have femur and tibial epiphyseal closure. TransCon CNP treatment will continue if femur and tibial epiphyseal closure is not confirmed at the age of 16 years for females, and 18 years for males. Treatment with TransCon CNP will be completed once femur and tibial epiphyseal closure is confirmed by radiographic imaging. The trial duration is individual for each trial participant. Visits will occur every 12-14 weeks throughout the trial.