Moses was considered the greatest prophet by the Jews. Honored as the greatest deliverer of the Jewish people and known as the "friend of God", it's not a stretch to think that there might be many similarities between his life and the life of Jesus. Here are a few of those parallels:
We could see his Moses's mother, but couldn't see his father
Both Moses and Jesus were born during a mandated slaughter of babies by insecure kings
Although born in Egypt, it was not the true home of Moses as his family was captive. Egypt became the home of Jesus for a short while as His family fled Harrod.
Moses was delivered by the water of the Nile into his destiny. Jesus from the waters of the Jordan into His.
Both originated in the halls of royalty in order to lead slaves to freedom
Both were shepherds of people.
In the story of Reuel, his daughters claimed "An Egyptian man rescued us." (Ex 2:17-19) Moses wasn't Egyptian – even though he probably looked like one. Jesus was not recognized by either the false shepherds, or the true shepherds.
Moses gave Reuel's ("friend of God") daughters water to drink. Jesus also provides water to those who will drink.
Moses was invited into Reuel's house and came in to live. This is what Jesus does, if invited.
Egypt represented sin, which Moses had to first enter in order to rescue the hostages. Jesus descended into the heart of the earth to set the captives free (Matt 12:40, 1 Pet 3:19).
Both died on a mountain before reaching the 'promised land'. For Jesus had to die before His kingdom could physically come to earth.
These are only a few of the more obvious similitudes. If you see some that I missed, please let me know!