Which Country Started The European Slave Trade With Africa?

Portugal, then Spain.hope this can help you

The first Official Shipment of African Slaves to Portugal was 1441. As has been discussed in some of the other answers, Slavery had been going on, as a consequence of conquest for Millenia. It was the Portuguese however who were credited with creating the European Slave Trade of Africans.

Portugal, then Spain

I'm sure it went on before then but it was common in ancient Greece and ancient Rome.  Slaves were taken from other European countries as well as the Middle East and, via Egypt, Nubian slaves were owned by Romans.  African slaves were a fairly common occurrence in ancient Greece and ancient Rome because north African traders sold them.  It wasn't only the Jews that were taken into slavery by the Egyptians!  Slavery was commonplace, not just between Europe and Africa but also within those continents.

It's wrong to assume that the trade was one way.  For around 400 years, the Barbary pirates raided Europe's southern and western coastal areas and took young prisoners to be sold into slavery with their own customers.  The Barbary Coast stretched from modern-day Tunisia round Morocco and down to Mauritania.  The European slaves were sold at markets in other Arab countries and some African countries.  Their range extended from Italy, along the French and Spanish coasts, along the western Atlantic coasts of Spain and France, as far north as the north-west tip of France, southwestern England and Ireland.  It was known as the "white slave trade" and fear of white slavery lingered for years.  

Portugal