The sentence is correct and usable in written English. You can use it when you are making a request to someone and hope they will view it positively. For example: "Good afternoon, I am writing to request an extension on my paper deadline. I hope you will consider my request favourably.".
I hope you will consider my application and will give me an opportunity of an interview.
I hope you will consider our request and remove the said story as soon as possible.
I hope you will consider that request.
"But I hope you will consider it," he said.
I hope you will consider reading this book.
I hope you will consider these proposals.
"I hope you'll consider Senator Clinton.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.