You can do this using groupby to group on the column of interest and then apply list to every group:

In [1]: df = pd.DataFrame( {'a':['A','A','B','B','B','C'], 'b':[1,2,5,5,4,6]})
        df

Out[1]: 
   a  b
0  A  1
1  A  2
2  B  5
3  B  5
4  B  4
5  C  6

In [2]: df.groupby('a')['b'].apply(list)
Out[2]: 
a
A       [1, 2]
B    [5, 5, 4]
C          [6]
Name: b, dtype: object

In [3]: df1 = df.groupby('a')['b'].apply(list).reset_index(name='new')
        df1
Out[3]: 
   a        new
0  A     [1, 2]
1  B  [5, 5, 4]
2  C        [6]