Average Cost. The average cost for a patio roof addition using low-maintenance wood-patterned aluminum runs for about $6,000 to $10,000 for an area of 20 by 20 feet, as of 2011. A screen can be added for an additional cost of $3,000 to $4,000.Adding a wood lattice roof can range between $500 and $10,000.There are other patio covers available that range from a $50 large outdoor umbrella to awnings that cost between $300 and $800.Mechanical awnings cost between $1,000 and $2,000. screen can be added for an additional cost of $3,000 to $4,000. Adding a wood lattice roof can range between $500 and $10,000. There are other patio covers available that range from a $50 large outdoor umbrella to awnings that cost between $300 and $800. Mechanical awnings cost between $1,000 and $2,000.