No, according to the subtitle to The Book of Mormon, it is "Another Testament of Jesus Christ", not another gospel.
Quoting from the title page of The Book of Mormon (emphasis mine):
Which is to show unto the remnant of the house of Israel what great things the Lord hath done for their fathers; and that they may know the covenants of the Lord, that they are not cast off forever—And also to the convincing of the Jew and Gentile that Jesus is the Christ, the Eternal God, manifesting himself unto all nations
From the Introduction:
It is a record of God’s dealings with ancient inhabitants of the Americas and contains the fulness of the everlasting gospel.
It contains the fulness of the everlasting gospel, not a new gospel. Continued (emphasis mine):
The record is now published in many languages as a new and additional witness that Jesus Christ is the Son of the living God and that all who will come unto Him and obey the laws and ordinances of His gospel may be saved.
One of the commenters asked what "Testament" means. From this, we see it means a witness, like a testimony.
When the record describes Christ visiting the Americas, He teaches basically the same Sermon on the Mount that He taught by the Sea of Galilee. And Jesus speaks of the people back in Jerusalem and why He came here to teach them the same gospel in the Americas, too.
It very much is the same gospel. Missionaries of the LDS Church preach by the Bible and Book of Mormon because the Book of Mormon does not replace the Bible; rather, they testify of each other and of the same Lord Jesus Christ.