A container with separate storage spaces includes a body for retaining a first substance therein and a sealing structure securely attached to the body for hermetically sealing the first substance in the body. The sealing structure has a sealing package hermetically enclosing a second substance, whereby the second substance can be released from the sealing package to be mixed with the first substance by cutting open the sealing package with a cutting member slidably cooperative with the sealing structure. With the use of the sealing structure, the container of this invention allows a person to refill the first substance to the body and replace a cut-open sealing package with a new one on his own, without need of manufacturer equipments.