Angular Material customize tab

Update

To customize tab background and ink bar, you can define your own theme then use the theme options on the tab group:

<div class="my-theme">
    <mat-tab-group [backgroundColor]="'primary'" [color]="'warn'">
        <mat-tab label="First"> Content 1 </mat-tab>
        <mat-tab label="Second"> Content 2 </mat-tab>
        <mat-tab label="Third"> Content 3 </mat-tab>
    </mat-tab-group>
</div>

Here is an example on StackBlitz.

Old answer with ::ng-deep

If you don't want to touch ViewEncapsulation, use ::ng-deep instead with class selector (inspect by browser dev tool).

For example (Angular 5, Material 2):

/* active tab */
::ng-deep .mat-tab-list .mat-tab-labels .mat-tab-label-active {
color:red;
background-color: green;
}

/* ink bar */
::ng-deep .mat-ink-bar {
background-color: var(--primary-color,#1F89CE) !important;
}

Latest Solution:-

1)Override in styles.css 2) Use selector of component of where that material-tab exists

styles.css

  app-child .mat-tab-label.mat-tab-label-active {
    padding: 0px 15px ;
  justify-content: flex-start;
  }

  app-child .mat-tab-label{
    padding: 0px 15px ;
  justify-content: flex-start;
  }

.mat-tab-group.mat-primary .mat-ink-bar, .mat-tab-nav-bar.mat-primary .mat-ink-bar{
    background:#6168e7;
  }

In your component, set ViewEncapsulation to None and add the styles in your component.css file.

Changes in Typescript code:

import {Component, ViewEncapsulation} from '@angular/core';

@Component({
  ....
  encapsulation: ViewEncapsulation.None
})

Component CSS:

/* Styles for tab labels */
.mat-tab-label {
    min-width: 25px !important;
    padding: 5px;
    background-color: transparent;
    color: red;
    font-weight: 700;
}

/* Styles for the active tab label */
.mat-tab-label.mat-tab-label-active {
    min-width: 25px !important;
    padding: 5px;
    background-color: transparent;
    color: red;
    font-weight: 700;
}

/* Styles for the ink bar */
.mat-ink-bar {
    background-color: green;
}

Demo