A Scottish Public Services Ombudsman (SPSO) report found "multiple failings in care and treatment" at Royal Aberdeen Children's Hospital.
The baby's mother complained about his care, after a medical device that relieves pressure on the brain was fitted shortly after he was born.
NHS Grampian said it apologised unreservedly.
The baby was born in October 2014, and was fitted with the device to drain excess fluid the following month.
The child was readmitted in August 2015 due to concern about his condition.
He was then transferred for specialist treatment in another health board area, but died on 12 August.
The SPSO said: "Our investigation determined that there was a lack of clarity regarding the roles of each medical team, and that there was a lack of communication between consultants when Baby A's condition was not improving.
"We also found that the neurosurgical team had not kept reasonable records, nor had they appropriately assessed Baby A before and after operations.
"We identified significant delays in Baby A being reviewed after he under went operations, and a delay in clinicians contacting the specialist centre for advice on the management of Baby A.
"Finally, we considered there to have been a lack of communication from the neurosurgical team and Baby A's parents."
NHS Grampian said in a statement: "It is clear we failed Baby A and therefore failed his family.
"The distress of the family was further compounded by the extremely poor standard of our communication with them.
"There can be no excuses for our conduct in this case and we apologise unreservedly.
"We accept all of the recommendations put forward by the Ombudsman in this case."
NHS Grampian has apologised after a 10-month-old baby died following serious failings in his care in Aberdeen.