Can I claim my grandchildren as dependants if I was the primary foster kinship for 10 months of the year?

[CatinaT1]

Yes, as a qualifying child, assuming you meet the other rules.

In order to claim a dependent on your tax return, the person must be your qualifying child or qualifying relative. Please see the requirements listed below. 

In order to be a qualifying child, the person must:   

• Be your son, daughter, stepchild, foster child, brother, sister, half-brother, half-sister, stepbrother, stepsister, or a descendant of any of them  
• Be under age 19 or under age 24 and a student at the end of the year OR permanently and totally disabled  
• Have lived with you for more than half of the year  
• Not have provided more than half of his or her own support  
• Not be filing a joint return for the year  

  

In order to be a qualifying relative, the person: 

  

• Can't be your qualifying child or the qualifying child of any other taxpayer 
• Must live with you all year as a member of your household or must be related to 
• Must have gross income of less than $4,200 for the year 
• You must provide more than half of the person's total support 

  

For more information on claiming a dependent, please see this TurboTax Help Article or IRS Publication 501. 

[Hal_Al]

Note that the requirement is that they lived with you for more than half of the year.  "Foster kinship for 10 months" is somewhat meaningless as being their grandparent already meets the relationship test.