I read from here (a Chinese website) that Martin Luther called John Calvin a son of the Devil.
Now I have never seen this quote anywhere. Did Luther say something like this to Calvin? If yes, why?
I cannot find a reference that he did, but it's possible he may have on a specific issue. From my research there is no evidence that he every called Calvin "the son of the Devil" and in fact those are Calvin's words, not Luther's.
Let's get some facts.
Calvin and Luther were contemporaries, both living in Europe during the early to mid 1500s. However, Luther was born in the 1480s and Calvin was born in 1509. Also, while both men were fluent in Latin, each wrote the majority of their works in their native tongues. Calvin in French, Luther in German.
However, it seems, while they had significant theological differences in many areas. Luther appreciated Calvin and Calvin appreciated Luther.
Luther and Calvin appreciated each other's work. In a letter to Bucer in Strasbourg in 1539, Luther sent his regards to Calvin. He mentioned that he had learned of a few of Calvin's writings. The Institutes was probably one of them. It is true that in many respects there is no difference between Calvin's ideas and that of Luther's, but it is not true that he is only a duplicate of Luther. Calvin had Luther as a starting point, and without difficulty, he remained loyal to his great predecessor. But at the same time, he also surpassed him, especially in his view of the Lord's Supper and church organization. In the history of church and culture, he has an independent place next to Luther. (1)
I think I may (however) have found the source of the quotation you refer to. These were not Luther's words, but Calvin's own:
Often have I been wont to declare, that even though he were to call me a devil, I should still not the less esteem and acknowledge him as an illustrious servant of God. (2)
This was a discussion of Luther's possible reaction to Calvin's views on the Lords Supper which were a marked contrast both from Rome's view but also Luther's. This was an acknowledgement both to how indebted he felt to Luther, and his strength of will that he was willing to disagree with Luther and potentially face his notorious wrath.
Likely this fear was motivated by the heated debates between Luther and Zwingli over the presence of Christ in communion.
At several points the debate was harsh and acrimonious. At other points the parties appeared to seek each other’s forgiveness for namecalling and for their breakdown of charity. (3)
There is little (if any) evidence that Luther ever addressed Calvin's position on the Lord's Supper specifically. However, due to the debates with Zwingli and Calvin's acknowledgement that his position was more similar to Zwingli's than Luther's he recognized that he certainly put himself in position to be the target of heated name calling or other insults from Luther.
(1) Martin Luther and John Calvin
(2) Schaff, History of the Christian Church, VII, p. 661.
(3) The Relation Between the Lutheran and Calvin Reformation
(4) Zwingli and Luther: The Giant vs. Hercules