Short Answer: God loves peace, created peace, and will make peace where it does not presently exist. This involves "going to war" with the enemies of peace.
The God of peace will soon crush Satan under your feet. -Romans 16:20
God of peace
The fruit of the Holy Spirit is peace. The nature of the Spirit and the nature of God are one and the same. In this way, God is the God of peace; this is His nature; His desire; His way.
Another way of seeing this truth is to read about Heaven, where God's ways are finally going to be followed completely. Passages such as Revelation 21:4 clearly paint Heaven as a place free of war.
We do not have peace
Clearly the Creation is not currently "at peace". (It's almost as if someone has corrupted His perfect design!) Clearly the wicked are not "at peace" with God and His people.
Who will separate us from the love of Christ? Will tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword? Just as it is written, “For Your sake we are being put to death all day long; We were considered as sheep to be slaughtered.” But in all these things we overwhelmingly conquer through Him who loved us. For I am convinced that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, nor powers, nor height, nor depth, nor any other created thing, will be able to separate us from the love of God, which is in Christ Jesus our Lord. -Romans 8:35-39
Unfortunately, not everyone wants to be at peace with God, with His ways, and with His people.
God will bring peace
To understand "the LORD is a man of war" we need to first consider who He is at war with.
And the nations were enraged, and Your wrath came, and the time came for the dead to be judged, and the time to reward Your bond-servants the prophets and the saints and those who fear Your name, the small and the great, and to destroy those who destroy the earth.”
The LORD is at war with those who destroy the earth. The wicked destroy the earth through sin; through rebellion against God's perfect, loving, peaceful ways; through attacking God's people; through attacking God.
God is going to "make things right" again, and bring peace to His people by putting an end to those who refuse to walk in peace.
Ultimately, God desires perfect peace - this was His original design in the beginning, and this will be the reality again when everything is "fixed". It is in this way that we need to understand God as the "God of peace." Presently, His Creation is full of "destroyers", but He will take care of them - and it is in this way that we need to understand that "the LORD is a man of war."