As an employer, how can you improve and encourage employee with self-confidence problems?

By providing opportunities for him/her to demonstrate competency within their skill set(s).

By empowering the individual to contribute their idea's AND have them become integral to a solution.

By not judging, blaming or otherwise calling him/her out on said self-confidence concern.

By allowing him/her the opportunity to demonstrate or teach back either an impactful part of their function or role AND/OR having them teach something they are passionate about.

By appropriate praise and recognition.

By assigning him/her an impactful task.

By coaching and mentoring them (personal and professional development - key leadership and management principles).

Praise the employee more than you criticize them. Showing appreciation for even the smallest work done helps to naturally create a feel good factor and improve self confidence. Criticism especially harsh ones in most cases shatters self confidence. Also continuous training. Giving new knowledge to the employee always helps a lot

The employee should see that you place all trust in him and make him feel that he is an inspiration to the organization and to each person with the same strategy

By providing adequate training and then trusting them to do their jobs well allows them know you have faith in them and that they should have faith in themselves.

Facilitate them through counseling and learning sessions. Helps them through increasing their self-awareness and EQ. The assessment will help them to build and gain confidence. 

Give them independent decision power according to there level of responsibility and evaluate there decisions result after regular interval. 

By informing them how much of an asset they are in a company and that they are there because they are capable and qualified therefore they should own up to their work

As an employer it my duty to give them task and let them do and help them to complete those then they will gain self confidence.

As an employer. You should know one thing. Never demoralise your employee, never condemn them, fine you will have to correct and rebuke them at times. But always make them proud of what they are doing, praise them everytime they do something great. But, some employers are just too insecure and too proud to praise their employees. You should organise an award event in the company and bring everyone together. This is the best work ethics.

Show an employee with self-confidence that you value him as a person. Guide his behavior rather than his personality. Communicate to the employee your expectations of excellence. Tell him/her you recognize his/her skills and you expect his/her performance to match those abilities. And lastly provide appropriate training and professional development opportunities.

Is motivated by goals easy to investigate and follow-up in the implementation of the request to restore confidence in himself work on his promise that his place will not be compromised in the company