The move comes after an independent human resources audit found that some staff and volunteers felt they were being bullied.
The allegations came to light in a report by consultancy Managing Diversity Associates, hired to review how well the charity implemented its diversity and equal opportunities policy. MDA set up focus groups and in-depth interviews with 500 staff and volunteers.
Leigh Daynes, spokesman for the Red Cross, said: "A handful of the 500 people surveyed for the report expressed concern about the behaviour of a minority of staff and volunteers, who they felt were bullying."
No disciplinary action has been taken, he said, because none of those interviewed issued formal grievances.
"We rely on individuals bringing complaints under the grievance procedures," said Daynes. "Had an individual brought a grievance against another under the robust policies we have in place, we would have investigated and taken the appropriate action.
"But it was not necessarily the case that any individual was named. I am not aware that they were, and no formal complaints were made."
The last high-profile case of bullying in the voluntary sector was nearly two years ago, when staff at Samaritans accused the charity of perpetuating a culture of fear and intimidation.
But these are not isolated incidents, according to Tim Field, who runs advice service Bully Online. Field claimed bullying is rife in the sector - and in at least 98 per cent of cases, he said, the employer takes no action against bullying even when made aware of it.
MDA's report, published late last year, recommended that the Red Cross train staff to implement its existing policy and procedures on harassment and bullying. Daynes said this was being done "as a priority".
He said 60 people were being trained as facilitators, to carry out inductions for the rest of the staff on the sort of behaviour the charity expects at work, and ensure people know how to avail themselves of the grievance procedures.