pandas filling nans by mean of before and after non-nan values

Althogh in case of multiple nan's in a row it doesn't produce the exact output you specified, other users reaching this page may actually prefer the effect of the method interpolate():

df = df.interpolate()

print(df)
     val
0    1.0
1    2.5
2    4.0
3    5.0
4    7.5
5   10.0
6    1.0
7    2.0
8    5.0
9    6.3
10   7.7
11   9.0

Use ffill + bfill and divide by 2:

df = (df.ffill()+df.bfill())/2

print(df)
     val
0    1.0
1    2.5
2    4.0
3    5.0
4    7.5
5   10.0
6    1.0
7    2.0
8    5.0
9    7.0
10   7.0
11   9.0

EDIT : If 1st and last element contains NaN then use (Dark suggestion):

df = pd.DataFrame({'val':[np.nan,1,np.nan, 4, 5, np.nan, 
                          10, 1,2,5, np.nan, np.nan, 9,np.nan,]})
df = (df.ffill()+df.bfill())/2
df = df.bfill().ffill()

print(df)
     val
0    1.0
1    1.0
2    2.5
3    4.0
4    5.0
5    7.5
6   10.0
7    1.0
8    2.0
9    5.0
10   7.0
11   7.0
12   9.0
13   9.0